Question

A club swimming pool is 16 ft wide and 32 ft long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 324ft^(2) . How wide can the strip​ be?

Answer 1

The maximum width of the strip around the swimming pool can be 3 ft.

Step-by-step explanation:

To find the maximum width of the strip, we need to subtract the dimensions of the pool from the area of the pool plus the strip.

The area of the pool is 16 ft x 32 ft = 512 ft^2.

Let x be the width of the strip.

The area of the pool plus the strip is (16+2x) ft x (32+2x) ft

= (512+64x+4x^2) ft^2.

Setting this equal to 324 ft^2, we have 512+64x+4x^2 = 324.

Rearranging, we get 4x^2+64x-188 = 0.

Using the quadratic formula, x = (-b ± √(b^2-4ac)) / (2a), where a=4, b=64, and c=-188, we can calculate the solutions for x.

The two possible solutions are x = 3 ft or x = -47/2 ft.

Since a negative width does not make sense in this context, the maximum width of the strip can be 3 ft.