Factoring word problem

Question

An envelope is 6 inches longer than it is wide. The area is 27 square inches. Find the length and width of the envelope

Answer 1

Use the equation:  area = length x width

 

A = l x w

l = w + 6

 

Substitute for length

 

27 = w(w + 6)

27 = w² + 6w

w² + 6w - 27 = 0

 

Now factor

 

(w + 9)(w - 3) = 0

 

Now solve for w and add 6 to get the length.

 

(There are two answers for w, but only the positive one is correct!)