A floot of a swimming pool is rectangular in shape,has length 10x-3 metres and width 6x metres.A floor is to be tiled with square tiles each with side length x/5 metres. the total area of 50 square tiles is 20.48 meters.  calculate the perimeter of the swimming pool with all working out.

To solve this problem, we'll first break it down into steps:

### Step 1: Determine the Area of One Tile
The side length of each square tile is given as $ \frac{x}{5} $ meters. The area $ A_{\text{tile}} $ of one tile is then:

\[
A_{\text{tile}} = \left(\frac{x}{5}\right)^2 = \frac{x^2}{25} \text{ square meters}
\]

### Step 2: Determine the Total Area of 50 Tiles
We're given that the total area of 50 tiles is 20.48 square meters. So,

\[
50 \times A_{\text{tile}} = 20.48 \text{ square meters}
\]

Substituting the expression for $ A_{\text{tile}} $:

\[
50 \times \frac{x^2}{25} = 20.48
\]

Simplifying:

\[
2x^2 = 20.48
\]

\[
x^2 = \frac{20.48}{2} = 10.24
\]

Taking the square root of both sides:

\[
x = \sqrt{10.24} = 3.2 \text{ meters}
\]

### Step 3: Calculate the Dimensions of the Swimming Pool
The length of the swimming pool is:

\[
\text{Length} = 10x - 3 = 10(3.2) - 3 = 32 - 3 = 29 \text{ meters}
\]

The width of the swimming pool is:

\[
\text{Width} = 6x = 6(3.2) = 19.2 \text{ meters}
\]

### Step 4: Calculate the Perimeter of the Swimming Pool
The perimeter $ P $ of a rectangle is given by:

\[
P = 2(\text{Length} + \text{Width})
\]

Substituting the values:

\[
P = 2(29 + 19.2) = 2(48.2) = 96.4 \text{ meters}
\]

### Final Answer:
The perimeter of the swimming pool is **96.4 meters**.

Would you like further details or have any questions? Here are 5 related questions for practice:

1. How would the perimeter change if the width of the pool was increased by 2 meters?
2. What would be the area of the pool with the current dimensions?
3. If each tile costs $1.50, what would be the total cost to tile the entire pool floor?
4. How many tiles are needed to cover the entire pool floor?
5. What would be the perimeter if $ x $ was reduced by half?

**Tip:** Always double-check the units in your calculations to ensure consistency, especially when working with areas and perimeters.

A floor of a swimming pool is rectangular in shape, has length 10x-3 metres and width 6x metres. A floor is to be tiled with square tiles each with side length x/5 metres. The total area of 50 square tiles is 20.48 meters. Calculate the perimeter of the swimming pool with all working out.

Learn how to calculate the perimeter of a rectangular swimming pool with a detailed step-by-step solution. This problem involves algebraic manipulation and geometric concepts, including the area and perimeter formulas. Suitable for students in Grades 8-10.

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