# Thread: [SOLVED] Polynomials to solve for area

1. ## [SOLVED] Polynomials to solve for area

A rectangular garden is 5 feet longer than twice its width. It has a sidewalk 3 feet wide on two of its sides. The area of the sidewalk is 213 square feet. Find the dimensions of the garden.

2X +5 for length and x for width on the garden. x+ 3 and 2x+ 8 for the sidewalk.

_____________ feet squared.

Follow this example 80 x 120.

The answer is 21 x 47 but i'm not sure what formula was used.

Any help would be appreciated. Thanks

2. ## Diagram

So we end up with

$(w+3)(2w+8)-(w)(2w+5)=213$

$2w^2+14w+24-2w^2-5w=213$

$9w+24=213 \iff w=21$

so the length is

$l=2w+5=2(21)+5=47$

so w=21 and l=47

3. ## confused

Im confused, doesnt he say that the SIDEWALK has an area of 213, not the sidewalk inlcluding the garden?