Jennifer plans to fence a rectangular area around her rectangular swimming pool. The total area enclosed by the fence, including the pool, should be 5 times the area of the pool alone. The pool is 20 feet by 17 feet.
A.)What is the total area enclosed by the fence?
B.) fencing costs $8 per linear foot. Jennifer plans to build the fence so that the length of the fence will be 25 feet on the 20 foot side of the pool. What is the cost of the fencing with this plan?
C.) Jennifer decides that the cost of her original plan is to expensive. She wants to find the dimensions of the fence with the least cost. What is a formula, C(w), for the cost of the fence if the length of the fence is w feet on the 20 foot side of the pool?
Please Some help me with this problem!!!!!!!!!!!!!!!!!!!!!
just start by translating the facts into symbols.
(A)
the pool is 20 by 17, so its area is 340.
The total area will be 5 times that, or 1700.
(B)
the fence is 25 feet long, so its width is 1700/25 = 68 ft. The perimeter is thus 2(25+68) = 186 ft. At $8/ft that will cost $1488.
(C)
from (B) we know the cost is 8*2(w+1700/w).
C(w) = 16w + 27200/w
Don't know why it keeps mentioning the side along the length of the pool. All we care about is the fence, not its relationship to the pool.
what is ti i have know idea please tell me the answer.
A.) To find the total area enclosed by the fence, including the pool, we can simply multiply the area of the pool by 5. Given that the pool is 20 feet by 17 feet, the area of the pool alone is:
Area of pool = length × width = 20 feet × 17 feet = 340 square feet
Therefore, the total area enclosed by the fence is:
Total area = 5 × Area of pool = 5 × 340 square feet = 1700 square feet
So, the total area enclosed by the fence, including the pool, is 1700 square feet.
B.) To calculate the cost of the fencing, we need to know the length and the cost per linear foot. We are given that the length of the fence will be 25 feet on the 20-foot side of the pool. Since the pool is on the 17-foot side, we don't need to include fencing on that side for this calculation.
The length of the fence we need to consider is therefore 25 feet. Given that the cost of fencing is $8 per linear foot, we can calculate the cost using the formula:
Cost of fencing = Length of fence × Cost per linear foot
Cost of fencing = 25 feet × $8/foot = $200
So, the cost of the fencing with this specific plan is $200.
C.) To find the formula for the cost of the fence, C(w), where w is the length of the fence in feet on the 20-foot side of the pool, we need to consider two sides that require fencing: the length side (w feet) and the width side (17 feet).
The cost of fencing for the length side (w feet) is simply w times the cost per linear foot. Since it is the 20-foot side that has the fence, the cost for this side is $8 per linear foot.
The cost of fencing for the width side (17 feet) is a fixed value of 17 feet times the cost per linear foot, which is $8.
Therefore, the total cost of the fence, C(w), is:
C(w) = w × $8 + 17 feet × $8 = 8w + 136
So, the formula for the cost of the fence, C(w), is 8w + 136.