help with math problem please

Question

the length of a rectangular garden is 3 ft less than twice its width. The garden is surrounded by a path with a uniform width of 3ft. If the total area of the garen and path combined is 108 sq ft. what are the dimensions of the garden?

define any variables used.

Answer 1

L=2w-3

(w+6)(L+6)=108

(w+6)(2w-3+6)=108

(w+6)(2w+3)=108

expand

2w^2+3w+12w+18=108

2w^2+15w+18=108

2w^2+15w+18-108=0

2w^2+15w-90=0

use the quadratic formula

w=-15/4+/-.25sqr(225+720)

= -3.75 +/-.25sqr945

= about -3.75 + 7.7

= 3.95 feet wide

L= 7.9-3= 4.9 feet Long

width should be <4

L<5

(4+6)(5+6)=110 = about 108