Rectangular garden

Question

The length of the garden is 4 ft. more than its width. There is a 2 ft. cement border that is placed around the garden. The area of the garden is 320 square feet, including the border. What is the original dimension of the garden itself?

Answer 1

Length L = w+4 for width w

With the border, the dimensions are:

L+4 = w+4+4 = w+8

and

width w +4

Length*width = Area

(w+8)(w+4) = 320

w^2 + 12w + 32 = 320

w^2 + 12w - 288 = 0

( w + 24 )( w - 12 ) = 0

w+24=0 --> w=-24 disqualified

w-12=0 --->w=12

Length is 16, width is 12

With the border the dimensions are 20 by 16