A rectangular swimming pool is 8 meters long and 12 meters wide. A tile boarder of uniform width is to be built around the pool usinjg 120 square meters of tile. How wide should the boarder be? Round anser to the nearest hundredth.

Let x be the border width.

The area of border tile is
A = (8+2x)(12+2x)- 8*12
which is (outer area) - (pool area)
= 4x^2 + 40x + 96 - 96
= 4x^2+ 40 x = 120
Solve for x.
You can simplify that to
x^2 + 10x - 30 = 0
Factor that for the one positive root.

let the width of the border, note the spelling, be x m

then the whole pool area including the border is (8+2x)(12+2x) = 8(12) + 120
96 + 40x + 4x^2 = 216
x^2 + 10x -30 = 0

solve

I got x = 2.416 and some negative x number.

your correct

To find out how wide the border should be, we need to first calculate the area of the pool and then subtract it from the total area covered by the tiles. Let's break it down step by step:

1. Calculate the area of the pool: Since the pool is rectangular, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 8 meters and the width is 12 meters. So, the area of the pool is 8 meters * 12 meters = 96 square meters.

2. Subtract the area of the pool from the total tile area: We are given that the total area covered by the tiles is 120 square meters. So, we subtract the area of the pool from the total tile area: 120 square meters - 96 square meters = 24 square meters.

3. Calculate the width of the border: Since the border is uniform in width, we can assume that the width of the border is the same on all sides. Let's denote the width of the border as "x". We know that the border will surround the pool, so the total length of the pool with the border will be the original length (8 meters) plus twice the width of the border (2x), and the total width will be the original width (12 meters) plus twice the width of the border (2x).

Therefore, the total area covered by the tiles, including the pool and the border, can be calculated by multiplying the new length with the new width: (8 meters + 2x) * (12 meters + 2x).

4. Set up an equation and solve for the width of the border: We need to solve for "x" in the equation: (8 + 2x) * (12 + 2x) = 24.
Expanding this equation gives us: 96 + 16x + 24x + 4x^2 = 24.
Rearranging the equation: 4x^2 + 40x + 96 = 24.
Subtracting 24 from both sides: 4x^2 + 40x + 72 = 0.

Now, this quadratic equation can be solved to find the values of "x", which represents the width of the border. Using factoring or the quadratic formula can yield the following solutions: x = -6 and x = -3.
Since we are looking for a positive width for the border, we discard the negative value of -3, and keep x = -6.

5. Find the positive width of the border: The positive value of x represents the width of the border. However, since width cannot be negative, we use the negative value as long as it is rounded to the nearest hundredth. So, the width of the border should be approximately 6.00 meters (rounded to the nearest hundredth).

Therefore, the width of the border should be approximately 6.00 meters.