Question 189231
The area of the garden is given by 17 x 11 = 187

If x=width of the path then the dimensions of the garden with the path would be:

(17+2x) long by (11+2x) wide (remember that the width of the path would add to all 4 sides)

The whole garden can have the maximum area of 288+187= square feet, so:

(2x+17)*(2x+11)=475

{{{4x^2+56x+187=475}}}

Subtracting 475 from both sides, we get:

{{{4x^2+56x-288=0}}}

Factoring, we get:

{{{(2x+36)*(2x-8)=0}}}

2x+36=0 and/or 2x-8=0

2x=-36          2x=8
x=-18           x=4

We take 4, since the width of the path cannot be negative.

The width of the path is 4 feet.