The area of a rectangle is 52m^2, and the length of the rectangle is 5m less than twice the width. Find the dimensions of the rectangle.

Question

This is a college algebra course question that I need help with. Please assist. 

Answer 1

width=w

length=2w-5

A=lw

52=w(2w-5)

52=2w²-5w

2w²-5w-52=0

2*52=2*2*2*13 and 13-8=5

(2w-13)(w+4)=0

2w-13=0 (w+4 yields a negative number which you disregard)

2w=13

w=6.5 m

2w-5=13-5=8 m

the dimensions are 6.5 m by 8 m

check:8*6.5=52 m²