SOLUTION: A rectangular patio is 7 feet longer than it is wide. Determine the dimensions of the patio if it measures 13 feet diagonally. Name the variables in the equation. Thank You

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Question 191722This question is from textbook
: A rectangular patio is 7 feet longer than it is wide. Determine the dimensions of the patio if it measures 13 feet diagonally. Name the variables in the equation.
Thank You This question is from textbook

Found 2 solutions by RAY100, solver91311:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
use right triangle with sides (w) by (w+7) with hyp of 13
pythagorous gives c^2 = a^2 + b^2
13^2 = (w)^2 + (w+7)^2
169 = w^2 + w^2 +14w +49
subtracting 169 both sides
0 = 2 w^2 + 14w -120
0= 2 (w^2 +7w -60)
factoring
0 = 2 ( w+12) (w-5)
set (w+12) = 0, w= -12 not realistic
set (w-5) = 0, w = 5
Dims are w=5, w+7 = 12
check 13^2 = 5^2 +12^2 = 25 +144 = 169 ok

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

First thing, you do this one in your head. 5 - 12 - 13 is a Pythagorean Triple and 5 and 12 differ by 7. Therefore the width is 5 and the length is 12.

But since you have to have an equation and name the variables...

Let x represent the width.

Then x + 7 has to be the length.

Since the diagonal of a rectangle forms a right triangle with the the length and the width, Pythagoras tells us you can say:

Factor and solve for x. Exclude the extraneous negative root.

John