The Area of a rectangle is 64m^2, The length is 2 less than double the width. What is the length and width.

Question

This was in my exam today and I’d like to know what the answer was thanks!

Answer 1

Let w = the width

Let 2w - 2 = the length

A = lw

64 = w(2w - 2)

64 = 2w^2 - 2w

0 = 2w^2 - 2w - 64

Divide both sides by 2.

w^2 - w - 32 = 0

w = 1 + sqrt(1 + 128)

2

w = 1 + sqrt(129)

2

length = 2w - 2 = 2[1 + sqrt(129)] - 2

2

length = 1 + sqrt(129) - 2

length = sqrt(129) - 1

Believe it or not, these answers actually check. :)

Very long problem to put on an exam.