Answer:
The walkway should be 2ft wide.
Explanation:
Let x be the width of the walkway surrounding the pool.
The area including the pool is 560ft².
Let's solve for the value of x.
The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.
A = lw
560 = (24 + 2x)(16 + 2x)
560 = 384 + 48x + 32x + 4x²
4x² + 80x + 384 - 560 = 0
4x² + 80x - 176 = 0
Divide the whole equation by 4
x² + 20x - 44 = 0
(x + 22)(x -2) = 0
x = -22; x = 2
Since we are dealing with dimensions, take the one with the positive value.
x = 2ft
Let's check
560ft² = (24ft + 2x)(16ft + 2x)
560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))
560ft² = (24ft + 4ft)(16ft + 4ft)
560ft² = (28ft)(20ft)
560ft² = 560ft² ✔