Finding the rectangle dimension

Question

I was given the diagonal of 5 ft. and the perimeter being 14. What are the steps into finding the dimension?

Answer 1

Since the perimeter is 14, 2L + 2W = 14 or L = (14 - 2W)/2 or L = 7 - W

Since the diagonal is 5, using the Pythogorean Theorem, W² + L² = 5².

Plug "7 - W" (from the first equation) into the second equation wherever there is an L giving you:

W² + (7 - W)² = 25 and solve for W. You will get two answers. Then plug those values into the first equation to get the corresponding L values.