SOLUTION: When you measured your diagonal clothesline across your rectangular porch, you found that it was 1 foot longer than the length of the porch, and 8 ft longer than the width. What ar

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Question 101842: When you measured your diagonal clothesline across your rectangular porch, you found that it was 1 foot longer than the length of the porch, and 8 ft longer than the width. What are the dimensions of your porch?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
let d be the diagonal of the porch.
it is also the hypotenuse of a right triangle.
d=L+1...L=d-1
d=W+8...W=d-8
L^2+W^2=d^2 (pythagorean theorum)
(d-1)^2+(d-8)^2=d^2
d^2-2d+1+d^2-16d+64=d^2 Expand.
2d^2-18d+65=d^2 Combine terms.
d^2-18d+64=0 Subtract d^2 from each side.
(d-13)(d-5)=0
d=13' diagonal of the porch.
d=5 not an answer in this problem because W=d-8=5-8=-3 and W cannot be negative.
L=12' by W=5' are the dimensions fo the porch. Answer
.
Check:
For d=13 L=13-1=12 W=13-8=5
12^2+5^2=144+25=169 13^2=169
Ed