The area of a rectangle is 28 yd^2, and the length of the rectangle is 1 yd more than twicw the width. find the demensions

Question

 I want to find the length and the width

 

Answer 1

Lw = 28

 

L = 2w + 1

 

Substitute 2w+1 in place of L in 1st equation to solve for width

 

w(2w+1) = 28

2w² + w = 28

2w² + w - 28 = 0

 

This can be factored by grouping;

2(-28) = -56... Factors of -56 that add to 1 are 8(-7).

Replace w with 8w - 7w and factor.

 

2w² + 8w - 7w - 28 = 0

2w(w+4) -7(w+4) = 0

(2w-7)(w+4) = 0

 

Either 2w-7 = 0 and w = 7/2 or 3.5

Or w+4 = 0 and w = -4

 

Discarding the negative, the width is 3.5 yds

 

L = 2w + 1 = 8 yds for length