A homeowner is installing a swimming pool in his backyard. he want its length to be 4 feet longer than its width. then he wants to surround it with a concrete walkway 3 feet wide. if he can only afford 300 square feet of concrete for the walkway, what should the dimensions for the pool be?

1. You have that:

- The homeowner want the length of the swimming pool to be 4 feet longer than its width.

- He wants to surround it with a concrete walkway 3 feet wide.

- He can only afford 300 square feet of concrete for the walkway.

2. Therefore, the tota area is:

At=L2xW2

L2 is the lenght of the walkway (L2=L1+3+3⇒L2 = (W1+4+6) ⇒L2=W1+10).

W2 is the width of the walkway (W1+3+3⇒W2=W1+6)

3. The area of the walkway is:

A2=At-A1

A2=300 ft²

4. Therefore, you have that the width of the swimming pool is:

A2 = (W1+10) (W1+6) - (W1+4) (W1)

300 = (W1²+6W1+10W1+60) - (W1²+4W1)

W1²+16W1+60-W1²-4W1-300=0

12W1-240=0

W1=240/12

W1=20 ft

5. And the length is:

L1=W1+4

L1=20+4

L1=24 ft