How can I deduce the hypotenuse from the information given?











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I'm going into Machine Learning and am currently brushing up on some Calculus on Coursera. Everything was going smoothly until I got to this word problem:




A ladder rests against a wall. The top of the ladder touches the wall at height $12$ meters. The length of the ladder is $4$ meters longer than the distance from the base of the ladder to the wall. Find the length of the ladder.




I am confused as to how to deduce the hypotenuse from the information given above. And have sat here trying different things with no success. What am I missing?






calculus algebra-precalculus trigonometry







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Edward Severinsen is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • I added the "algebra-precalculus" tag to your post. Cheers!
    – Robert Lewis
    4 hours ago










  • Draw a picture with the ladder. Label the sides of the triangle formed by the ladder, the wall, and the floor. If you call the base x, the ladder is x+4. Then use the Pythagorean theorem.
    – Joel Pereira
    4 hours ago















up vote
2
down vote

favorite
1












I'm going into Machine Learning and am currently brushing up on some Calculus on Coursera. Everything was going smoothly until I got to this word problem:




A ladder rests against a wall. The top of the ladder touches the wall at height $12$ meters. The length of the ladder is $4$ meters longer than the distance from the base of the ladder to the wall. Find the length of the ladder.




I am confused as to how to deduce the hypotenuse from the information given above. And have sat here trying different things with no success. What am I missing?






calculus algebra-precalculus trigonometry







share|cite|improve this question









New contributor




Edward Severinsen is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • I added the "algebra-precalculus" tag to your post. Cheers!
    – Robert Lewis
    4 hours ago










  • Draw a picture with the ladder. Label the sides of the triangle formed by the ladder, the wall, and the floor. If you call the base x, the ladder is x+4. Then use the Pythagorean theorem.
    – Joel Pereira
    4 hours ago













up vote
2
down vote

favorite
1









up vote
2
down vote

favorite
1






1





I'm going into Machine Learning and am currently brushing up on some Calculus on Coursera. Everything was going smoothly until I got to this word problem:




A ladder rests against a wall. The top of the ladder touches the wall at height $12$ meters. The length of the ladder is $4$ meters longer than the distance from the base of the ladder to the wall. Find the length of the ladder.




I am confused as to how to deduce the hypotenuse from the information given above. And have sat here trying different things with no success. What am I missing?






calculus algebra-precalculus trigonometry







share|cite|improve this question









New contributor




Edward Severinsen is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I'm going into Machine Learning and am currently brushing up on some Calculus on Coursera. Everything was going smoothly until I got to this word problem:




A ladder rests against a wall. The top of the ladder touches the wall at height $12$ meters. The length of the ladder is $4$ meters longer than the distance from the base of the ladder to the wall. Find the length of the ladder.




I am confused as to how to deduce the hypotenuse from the information given above. And have sat here trying different things with no success. What am I missing?






calculus algebra-precalculus trigonometry




calculus algebra-precalculus trigonometry






share|cite|improve this question









New contributor




Edward Severinsen is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Edward Severinsen is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




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edited 4 hours ago









Key Flex

7,12441229




7,12441229






New contributor




Edward Severinsen is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 4 hours ago









Edward Severinsen

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1133




New contributor




Edward Severinsen is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Edward Severinsen is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Edward Severinsen is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • I added the "algebra-precalculus" tag to your post. Cheers!
    – Robert Lewis
    4 hours ago










  • Draw a picture with the ladder. Label the sides of the triangle formed by the ladder, the wall, and the floor. If you call the base x, the ladder is x+4. Then use the Pythagorean theorem.
    – Joel Pereira
    4 hours ago


















  • I added the "algebra-precalculus" tag to your post. Cheers!
    – Robert Lewis
    4 hours ago










  • Draw a picture with the ladder. Label the sides of the triangle formed by the ladder, the wall, and the floor. If you call the base x, the ladder is x+4. Then use the Pythagorean theorem.
    – Joel Pereira
    4 hours ago
















I added the "algebra-precalculus" tag to your post. Cheers!
– Robert Lewis
4 hours ago




I added the "algebra-precalculus" tag to your post. Cheers!
– Robert Lewis
4 hours ago












Draw a picture with the ladder. Label the sides of the triangle formed by the ladder, the wall, and the floor. If you call the base x, the ladder is x+4. Then use the Pythagorean theorem.
– Joel Pereira
4 hours ago




Draw a picture with the ladder. Label the sides of the triangle formed by the ladder, the wall, and the floor. If you call the base x, the ladder is x+4. Then use the Pythagorean theorem.
– Joel Pereira
4 hours ago










2 Answers
2






active

oldest

votes

















up vote
2
down vote



accepted










Let $d$ be the distance from the ladder to the wall, and $l$ the length of the ladder.
Then



$l = d + 4; tag 1$



since the wall is mos' likely perpendicular to the ground, we may deploy the Pythagorean theorem and write



$l^2 = (12)^2 + d^2; tag 2$



substituting (1) into (2) yields



$(d + 4)^2 = 144 + d^2, tag 3$



$d^2 + 8d + 16 = 144 + d^2, tag 4$



$8d + 16 = 144 Longrightarrow 8d = 128 Longrightarrow d = 16M Longrightarrow l = 20M. tag 5$






share|cite|improve this answer

















  • 1




    Oh my. I distributed the 2 exponent to d and 4 individually instead of multiplying the expression by itself. Not the first time this has gotten me.
    – Edward Severinsen
    4 hours ago










  • @EdwardSeverinsen: we're all learners, my friend!
    – Robert Lewis
    4 hours ago


















up vote
4
down vote













enter image description here



Given the length of the wall as $12$.



Take the length of the base as $x$.



Since, the length of the ladder is $4$ times greater than the base we have $x+4$



Now according to the pythagorean theorem we have,



$$(x+4)^2=12^2+x^2$$
$$x^2+16+8x=144+x^2$$
$$8x=128$$
$$x=16$$



So, the length of the ladder $=x+4implies 16+4=20$






share|cite|improve this answer

















  • 2




    Nice graphic, +1!
    – Robert Lewis
    4 hours ago






  • 1




    @RobertLewis Thanks!
    – Key Flex
    4 hours ago











Your Answer





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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote



accepted










Let $d$ be the distance from the ladder to the wall, and $l$ the length of the ladder.
Then



$l = d + 4; tag 1$



since the wall is mos' likely perpendicular to the ground, we may deploy the Pythagorean theorem and write



$l^2 = (12)^2 + d^2; tag 2$



substituting (1) into (2) yields



$(d + 4)^2 = 144 + d^2, tag 3$



$d^2 + 8d + 16 = 144 + d^2, tag 4$



$8d + 16 = 144 Longrightarrow 8d = 128 Longrightarrow d = 16M Longrightarrow l = 20M. tag 5$






share|cite|improve this answer

















  • 1




    Oh my. I distributed the 2 exponent to d and 4 individually instead of multiplying the expression by itself. Not the first time this has gotten me.
    – Edward Severinsen
    4 hours ago










  • @EdwardSeverinsen: we're all learners, my friend!
    – Robert Lewis
    4 hours ago















up vote
2
down vote



accepted










Let $d$ be the distance from the ladder to the wall, and $l$ the length of the ladder.
Then



$l = d + 4; tag 1$



since the wall is mos' likely perpendicular to the ground, we may deploy the Pythagorean theorem and write



$l^2 = (12)^2 + d^2; tag 2$



substituting (1) into (2) yields



$(d + 4)^2 = 144 + d^2, tag 3$



$d^2 + 8d + 16 = 144 + d^2, tag 4$



$8d + 16 = 144 Longrightarrow 8d = 128 Longrightarrow d = 16M Longrightarrow l = 20M. tag 5$






share|cite|improve this answer

















  • 1




    Oh my. I distributed the 2 exponent to d and 4 individually instead of multiplying the expression by itself. Not the first time this has gotten me.
    – Edward Severinsen
    4 hours ago










  • @EdwardSeverinsen: we're all learners, my friend!
    – Robert Lewis
    4 hours ago













up vote
2
down vote



accepted







up vote
2
down vote



accepted






Let $d$ be the distance from the ladder to the wall, and $l$ the length of the ladder.
Then



$l = d + 4; tag 1$



since the wall is mos' likely perpendicular to the ground, we may deploy the Pythagorean theorem and write



$l^2 = (12)^2 + d^2; tag 2$



substituting (1) into (2) yields



$(d + 4)^2 = 144 + d^2, tag 3$



$d^2 + 8d + 16 = 144 + d^2, tag 4$



$8d + 16 = 144 Longrightarrow 8d = 128 Longrightarrow d = 16M Longrightarrow l = 20M. tag 5$






share|cite|improve this answer












Let $d$ be the distance from the ladder to the wall, and $l$ the length of the ladder.
Then



$l = d + 4; tag 1$



since the wall is mos' likely perpendicular to the ground, we may deploy the Pythagorean theorem and write



$l^2 = (12)^2 + d^2; tag 2$



substituting (1) into (2) yields



$(d + 4)^2 = 144 + d^2, tag 3$



$d^2 + 8d + 16 = 144 + d^2, tag 4$



$8d + 16 = 144 Longrightarrow 8d = 128 Longrightarrow d = 16M Longrightarrow l = 20M. tag 5$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 4 hours ago









Robert Lewis

42.5k22862




42.5k22862








  • 1




    Oh my. I distributed the 2 exponent to d and 4 individually instead of multiplying the expression by itself. Not the first time this has gotten me.
    – Edward Severinsen
    4 hours ago










  • @EdwardSeverinsen: we're all learners, my friend!
    – Robert Lewis
    4 hours ago














  • 1




    Oh my. I distributed the 2 exponent to d and 4 individually instead of multiplying the expression by itself. Not the first time this has gotten me.
    – Edward Severinsen
    4 hours ago










  • @EdwardSeverinsen: we're all learners, my friend!
    – Robert Lewis
    4 hours ago








1




1




Oh my. I distributed the 2 exponent to d and 4 individually instead of multiplying the expression by itself. Not the first time this has gotten me.
– Edward Severinsen
4 hours ago




Oh my. I distributed the 2 exponent to d and 4 individually instead of multiplying the expression by itself. Not the first time this has gotten me.
– Edward Severinsen
4 hours ago












@EdwardSeverinsen: we're all learners, my friend!
– Robert Lewis
4 hours ago




@EdwardSeverinsen: we're all learners, my friend!
– Robert Lewis
4 hours ago










up vote
4
down vote













enter image description here



Given the length of the wall as $12$.



Take the length of the base as $x$.



Since, the length of the ladder is $4$ times greater than the base we have $x+4$



Now according to the pythagorean theorem we have,



$$(x+4)^2=12^2+x^2$$
$$x^2+16+8x=144+x^2$$
$$8x=128$$
$$x=16$$



So, the length of the ladder $=x+4implies 16+4=20$






share|cite|improve this answer

















  • 2




    Nice graphic, +1!
    – Robert Lewis
    4 hours ago






  • 1




    @RobertLewis Thanks!
    – Key Flex
    4 hours ago















up vote
4
down vote













enter image description here



Given the length of the wall as $12$.



Take the length of the base as $x$.



Since, the length of the ladder is $4$ times greater than the base we have $x+4$



Now according to the pythagorean theorem we have,



$$(x+4)^2=12^2+x^2$$
$$x^2+16+8x=144+x^2$$
$$8x=128$$
$$x=16$$



So, the length of the ladder $=x+4implies 16+4=20$






share|cite|improve this answer

















  • 2




    Nice graphic, +1!
    – Robert Lewis
    4 hours ago






  • 1




    @RobertLewis Thanks!
    – Key Flex
    4 hours ago













up vote
4
down vote










up vote
4
down vote









enter image description here



Given the length of the wall as $12$.



Take the length of the base as $x$.



Since, the length of the ladder is $4$ times greater than the base we have $x+4$



Now according to the pythagorean theorem we have,



$$(x+4)^2=12^2+x^2$$
$$x^2+16+8x=144+x^2$$
$$8x=128$$
$$x=16$$



So, the length of the ladder $=x+4implies 16+4=20$






share|cite|improve this answer












enter image description here



Given the length of the wall as $12$.



Take the length of the base as $x$.



Since, the length of the ladder is $4$ times greater than the base we have $x+4$



Now according to the pythagorean theorem we have,



$$(x+4)^2=12^2+x^2$$
$$x^2+16+8x=144+x^2$$
$$8x=128$$
$$x=16$$



So, the length of the ladder $=x+4implies 16+4=20$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 4 hours ago









Key Flex

7,12441229




7,12441229








  • 2




    Nice graphic, +1!
    – Robert Lewis
    4 hours ago






  • 1




    @RobertLewis Thanks!
    – Key Flex
    4 hours ago














  • 2




    Nice graphic, +1!
    – Robert Lewis
    4 hours ago






  • 1




    @RobertLewis Thanks!
    – Key Flex
    4 hours ago








2




2




Nice graphic, +1!
– Robert Lewis
4 hours ago




Nice graphic, +1!
– Robert Lewis
4 hours ago




1




1




@RobertLewis Thanks!
– Key Flex
4 hours ago




@RobertLewis Thanks!
– Key Flex
4 hours ago










Edward Severinsen is a new contributor. Be nice, and check out our Code of Conduct.










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