Answer:
- perimeter: 234 ft
- area: 3150 ft²
Step-by-step explanation:
You want the perimeter and area of the largest rectangle that will fit in an area 48 ft by 81 ft with a 3 ft wide border all around.
Pool Dimensions
The width of the pool will be 48 ft less a 3 ft border on one side and a 3 ft border on the other side. That is, its width will be 48 -3 -3 = 42 ft.
Similarly, the length will be 81 -3 -3 = 75 ft.
Perimeter
The perimeter of a rectangle is given by the formula ...
P = 2(L +W)
P = 2(75 ft +42 ft) = 2(117 ft) = 234 ft
The perimeter of the largest pool is 234 feet.
Area
The area of a rectangle is given by the formula ...
A = LW
A = (75 ft)(42 ft) = 3150 ft²
The area of the largest pool is 3150 ft².
__
Additional comment
The distance formula can be used to find the side lengths from the corner coordinates. Here, we don't need to do that.
