The length of a rectangle is 8 less than twice the width. The area of the rectangle is 123 cm^2, what is the length of the diagonal?

Question

Step by step will be much helpful for me to follow along.

Answer 1

123=Lw= (2w-8)w= 2w^2 -8w

2w^2-8w -123=0

w = 8/4 +/- (1/4)sqr(64+984)

w = 2+/- sqr(1044)4

w = 10.07775

L = 123/2 = 123/10.07775 = about 12.205

D^2 = L^2 + w^2 = 148.965 + 101.56

D^2 = 250.525

D= sqr250.525= about 15.83 cm = the diagonal

Answer 2

The diagonal creates a right triangle the area of which is one-half the area of the rectangle. This from Geometry. Draw and label a diagram!

61.5² = w² + (2w - 8)²

Can you solve for w and answer?