A rectangular swimming pool is bordered by a concrete patio. The width of the patio is the same on every side. The area of the surface of the pool is equal to the area of the patio. What is the width of the patio?

(Length of Pool: 24 Width of Pool: 16)

its 4

To find the width of the patio, we first need to calculate the area of the pool. The area of a rectangle can be determined by multiplying its length by its width. In this case, the length of the pool is 24 and the width is 16. Therefore, the area of the pool is 24 * 16 = 384 square units.

Since the area of the pool is equal to the area of the patio, the width of the patio can be determined by subtracting the width of the pool from the total width of the rectangle. In this case, since the pool is surrounded by the patio on all sides, the total width of the rectangle would be the width of the pool plus twice the width of the patio. Let's represent the width of the patio as 'w'. Therefore, the total width of the rectangle would be 16 + 2w.

Now we can set up an equation to find the width of the patio. The equation would be: 16 + 2w = 384. We subtract 16 from both sides to isolate 2w, and then divide by 2 to solve for w. It would look like this:

2w = 384 - 16
2w = 368
w = 368 / 2
w = 184

So, the width of the patio is 184 units.

ty

let the width of the border be x units

length of whole thing = 24+2x
width of whole thing = 16+2x

area of whole thing = (24+2x)(16+2x)

since pool = patio
whole thing = twice pool
(24+2x)(16+2x) = 2(24)(16)

solve the quadratic