The width of a rectangle is 1 less than twice its length. If the area of the rectangle is 65 cm 2 , what is the length of the diagonal?

Answer 1

w = 2L-1

Lw = 65 cm^2

(2L-1)L = 65 = 2L^2 -L

2L^2 - L -65 = 0

L = 1/4 + .25sqr(1 +8(65) = .25 + .25sqr521

w = 2L-1 = .5 +.5sqr521 -1

d^2 = L^2 +w^2

diagonal length = d = sqr((.25 + .25sqr521)^2 + (.5sqr521 - .5)^2)= about 12.432436 cm