Question

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?

Answer 1

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