We have to figure out the length and width of the rectangle. To get there, we have to start with the formula for calculating perimeter:
P = 2L + 2W
Here, we're using P for perimeter, L for length, and W for width.
We know something about the relationship between the rectangle's width and its length. The problem tells us that the width is 15 feet less than one-half the length. So:
W = 0.5L - 15
We can substitute that into our formula to calculate perimeter:
P = 2L + 2W
P = 2L + 2 (0.5L - 15)
P = 2L + L - 30
P = 3L - 30
The problem also tells us that the perimeter is 66 feet. So now we can substitute that value for P:
66 = 3L - 30
96 = 3L
L = 32 feet
Since the length is 32 feet, and the width is 15 feet less than one-half the length:
W = 0.5L - 15
W = 0.5(32) - 15
W = 16 - 15 = 1 foot
Now we check our answer. Let's go back to the perimeter formula to do that:
P = 2L + 2W
P = 2 (32) + 2(1)
P = 64 + 2 = 66 feet
We got it right!
