w is less than what is perimeter

Question

A rectangluer yard has area 96 square feet. If the width of the yard is 4 feet less than the length , what is the perimeter,IN feet, of the yard?

Answer 1

width: W

length: L

 

Area: A=W×L

Perimeter: P= 2W + 2L

 

L=W+4

A=96=W×L=W×(W+4) 

 

96=W²+4W

W²+4W-96=0

 

To solve this quadratic, I would recommend something I call the product sum method, where I find factors of a×c which sum to b. In this case,

1×(-96)=-96

-96=12×(-8)

        12+(-8)=4

So I'm going to split my middle term into 8-12, which doesn't change anything but is convenient for factoring

 

W²+4W        -96=0

W²+12W-8W-96=0

W(W+12)-8(W+12)=0

(W-8)(W+12)=0

 

The zero product property here says that W must be either 8 or -12, but we cannot have a distance dimension which is negative.

 

So W=8, which means L=12, which means

P=2W+2L=16+24=40