A Square Tile Is Used To Border The Perimeter Of A Seimming Pool…

a square tile is used to border the perimeter of a seimming pool 12 m by 8 m. It was required in border with tiles that bottom perimeter if the total area of the tiles installed as border is 42 sq m​

Answer:

First, we need to find the perimeter of the swimming pool.

Perimeter = 2(Length + Width)

Perimeter = 2(12 m + 8 m)

Perimeter = 2(20 m)

Perimeter = 40 m

Now, we need to find the area of the pool that will be covered by the tiles.

Area of the pool = Length x Width

Area of the pool = 12 m x 8 m

Area of the pool = 96 sq m

Let x be the length of one side of the square tile in meters.

If the tiles are used to border the perimeter of the pool, then the length of each side of the pool will be increased by twice the length of the tile, or 2x. Thus, the length and width of the pool with the border will be:

Length = 12 + 2x

Width = 8 + 2x

The area covered by the tiles will be the difference between the area of the pool with the border and the area of the original pool:

Area of tiles = (Length x Width) – (12 m x 8 m)

42 sq m = [(12 + 2x) x (8 + 2x)] – 96 sq m

Simplifying this equation, we get:

42 sq m = 16x + 4x^2

Rearranging and solving for x, we get:

4x^2 + 16x – 42 = 0

Using the quadratic formula, we get:

x = (-16 ± sqrt(16^2 – 4(4)(-42))) / (2(4))

x = (-16 ± sqrt(1024 + 672)) / 8

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x = (-16 ± sqrt(1696)) / 8

x = (-16 ± 41.2) / 8

Since the length of a side cannot be negative, we take the positive solution:

x = (-16 + 41.2) / 8

x = 3.15

Therefore, the length of one side of the square tile is approximately 3.15 meters.

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