Respuesta :
Answer: the width of the walkway is 5 feet
Step-by-step explanation:
Let x represent the width of the walkway.
If the walkway must have a uniform width around the entire pool, it means that
The width of the total area would be x + 10 + x = 10 + 2x
The length of the total area would be x + 20 + x = 20 + 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 + 20)(x - 5) = 0
x = 5 or x = - 20
Since the width cannot be negative, then, the width of the walkway would be 5 feet on all sides.
