diagonal of a rectangle

Question

The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 193 , what is the length of the diagonal?

Answer 1

W=2L-5

Area = LW = L(2L-5) = 2L^2 -5L = 193

2L^2 -5L - 193 = 0

use the quadratic formula

L = 5/4 + or - (1/4)sqr(25+2(4)(193)) =about 11.15 cm long

W = 22.3-5 = 17.3 cm wide

D^2 = W^2 + L^2 = 17.3^2 + 11.15^2 = 423.7

D = diagonal length = sqr423.7 = about 20.6 cm