finding the length of the diagonal

Question

The width of a rectangle is 7 less than twice its length. If the area of the rectangle is 169 , what is the length of the diagonal? 

Answer 1

Let L = length, W = width, A = area andD = diagonal

W = 2L - 7

A = LW = L(2L -7) = 169

2L² - 7L - 169 = 0

The quadratic formula gives an extraneous root and L = 11.11 so that W = 15.22

You need the Pythagorean theorem to get the diagonal.