Question

A zookeeper wants to build an enclosure with a 3-foot wife moat (the shaded region) around it as shown in the diagram. She wants to use 96 feet of fencing to keep the visitors out of the moat, and 108 feet of fencing for the four sides of the inner fence. What should the dimensions of the inner fence be?

Answer 1

first minus 6 - 3 the answer is 3

Answer 2

Let's start by labeling the sides of the inner fence. Let's say the length of the enclosure is L and the width of the enclosure is W.
We know that the total amount of fencing needed for the outer fence (including the moat) is 96 feet. The moat has a width of 3 feet, so the perimeter of the outer fence is:
P_outer = 2(L+6) + 2(W+6) = 2L + 2W + 24
We also know that the total amount of fencing needed for the inner fence is 108 feet. The perimeter of the inner fence is:
P_inner = 2L + 2W
We can set up a system of equations to solve for L and W:
2L + 2W + 24 = 96 2L + 2W = 108
Simplifying the first equation, we get:
2L + 2W = 72
Now we can solve for L or W in terms of the other variable:
L = 36 - W
Substituting this into the second equation, we get:
2(36 - W) + 2W = 108
Simplifying, we get:
72 - 2W + 2W = 108
2W = 36
W = 18
Now we can substitute this value of W back into the equation we derived earlier:
L = 36 - W = 36 - 18 = 18
So the dimensions of the inner fence should be 18 feet by 18 feet.