Rectangle question

Question

the length of a rectangle is 3 feet longer than its width.  If the length is decreased by 3 feet and its width is increased by 2 feet, its area would be decreased by 8 square feet.  What is the length of the rectangle?

Answer 1

width = w

length =l = w+3

 

Area = length * width

a =l*w

 

a =(w+3)(w) =w² +3w

 

If the length is decreased by 3 feet and its width is increased by 2 feet,

Length =l-3=(w+3)-3 =w+3-3=w

width=w+2

area =a=w(w+2) =w²+2w

 

We know that

w² +3w > w²   +2w

 

w² + 3w  - 8 = w²+2w

 

w =8

l=83=11 feet