Question

Pool measuring 10 ft by 20 feet will have a cement walkway around it. The area covered by the pool and the cement walkway is 600 square feet. If the walkway must have a uniform width around the entire pool, what is the width of the walkway?

Answer 1

Answer:the width of the walkway is 5 feet

Step-by-step explanation:

Let x represent the width of the walkway.

The pool measures 10 ft by 20. If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway would be 10 + x + x = 10 + 2x

The total width of the pool and the walkway would be 20 + x + x = 10 + 2x

The area covered by the pool and the cement walkway is 600 square feet. This means that

(10 + 2x)(20 + 2x) = 600

200 + 20x + 40x + 4x^2 = 600

4x^2 + 60x + 200 - 600 = 0

4x^2 + 60x - 400 = 0

Dividing through by 4, it becomes

x^2 + 15x - 100 = 0

x^2 + 20x - 5x - 100 = 0

x(x + 20) - 5(x + 20) = 0

(x - 5)(x + 20) = 0

x = 5 or x = - 20

The width cannot be negative. Therefore, the width of the walkway is 5 feet