SOLUTION: use let statements. Show All work and All steps. The diagonal of a picture frame is 13 inches. If the length of the frame is 7 inches greater than it's width, find the dimension

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Question 966128: use let statements. Show All work and All steps.
The diagonal of a picture frame is 13 inches. If the length of the frame is 7 inches greater than it's width, find the dimensions of the frame.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
W=width; L=length=W+7in; D=diagonal
The diagonal of a rectangle forms the hypotenuse of a right triangle with the length and width as legs, so:
.
L%5E2%2BW%5E2=D%5E2 Substitute for L
%28W%2B7in%29%5E2%2BW%5E2=%2813in%29%5E2
%28W%5E2%2B14W%2B49%29%2BW%5E2=169in%5E2%0D%0A%7B%7B%7B2W%5E2%2B14W%2B49=169in%5E2 Subtract 169in^2 from each side.
2W%5E2%2B14W-120=0 Divide each side by 2.
W%5E2%2B7W-60=0
%28W%2B12%29%28W-5%29=0
W%2B12=0 or W-5=0
W=-12 or W=5
ANSWER 1: The width of the frame is 5 inches.
.
L=W+7in=5in+7in=12in
ANSWER 2: The length of the frame is 12 inches.
.
CHECK:
L%5E2%2BW%5E2=D%5E2
%2812in%29%5E2%2B%285in%29%5E2=%2813in%29%5E2
144in%5E2%2B25in%5E2=169
169in%5E2=169in%5E2