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?
- The homeowner<span> want the length of the swimming pool to be 4 feet longer than its width.</span> - 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
