Quadratic Equation Stuff

Question

The width of a rectangle is 2 less than twice its length. If the area of the rectangle is 175 cm2, what is the length of the diagonal?

The length of the diagonal is how many cm?

Answer 1

w =2L-2

A=wL =175 = (2L-2)L = 2L^2 -2L

L^2 -2L = 87.5

L^2 -2L +1 = 88.5

(L-1)^2 = 88.5

L = 1 +sqr88.5 = about 10.41 cm

w =20.82-2 = 18.82 cm

diagonal = d

d^2 = about 18.82^2 + 10.41^2 = 462.56

d = sqr462.56= about 21.51 cm diagonal