An inequality must be written describing the dimensions of the pool.

Question

A rectangular swimming pool is 4 meters longer than it is wide and is surrounded by a deck 2 meters wide on all sides. The area of the pool and deck together is at least 140 square meters greater than the area of the pool alone. Write an inequality to describe the dimensions of the pool.

Answer 1

L= length of the pool

W=width of the pool

L= 4+W

A_pool = L•W = (4+W)•W= 4W +W²

A_{pool & deck} = (4+W+2+2)•(W+2+2) = (W+8)•(W+4) = W² + 12W + 32

W²+12W+32 ≥ W² +4W +140

12W+32≥ 4w+140

8W≥108

W≥13.5 meters

L≥17.5 meters