Your parents decide they would like to install a rectangular swimming pool in the backyard. There is a 15-foot by 20-foot rectangular area available. Your parents request a 3-foot edge around each side of the pool. Draw a diagram of this situation in a coordinate plane. What is the perimeter and area of the largest swimming pool that will fit?

Step-by-step explanation:

Since the 3 ft edge is on both sides of the pool, each dimension of the pool is 6 ft shorter than the corresponding dimension of the space. The pool will be 15 ft -6 ft = 9 ft in one direction and 20 ft -6 ft = 14 ft in the other direction.

The perimeter of the pool is the sum of its side lengths:

  P = 9 ft + 14 ft + 9 ft + 14 ft = 2(9 ft +14 ft) = 2(23 ft)

  P = 46 ft

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The area of the pool is the product of its length and width:

  A = (14 ft)(9 ft) = 126 ft²

The perimeter and area are 46 ft and 126 ft², respectively.