Chapter 9: Similar Figures

Explain · page 183: Example 18: Falak plans to tile a square patio with an area of 100 square metres. He decides to use both square tiles and triangular tiles, each with an area of 0.25 square metres. If 60% of the tiles will be square and 40% will be triangular, how many tiles of each shape are needed?

To solve a problem like this, you first find the total number of items needed to cover a space, and then split that total into parts based on percentages. It helps you figure out exactly how many individual pieces of each shape you need to buy for a project.

Here are the key steps to keep in mind:

• Calculate the total count: Divide the total surface area (رقبہ) by the area of a single tile.
• Apply the percentages: Multiply the total tile count by each percentage (فیصد) to get the required number for each shape.
• Verify your answer: Add the amounts of square (مربع) tiles and triangular (مثلث) tiles together to make sure they equal the total number of tiles.

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Step-by-Step Solution

$$\text{Total number of tiles} = \frac{\text{Patio Area}}{\text{Tile Area}}$$

$$\text{Total number of tiles} = \frac{100}{0.25}$$

$$\text{Total number of tiles} = 400$$

$$\text{Number of square tiles} = 400 \times 60\%$$

$$\text{Number of square tiles} = 400 \times 0.6$$

$$\text{Number of square tiles} = \mathbf{240}$$

$$\text{Number of triangular tiles} = 400 \times 40\%$$

$$\text{Number of triangular tiles} = 400 \times 0.4$$

$$\text{Number of triangular tiles} = \mathbf{160}$$

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Real-Life Example

Imagine a shopkeeper in Anarkali Bazaar who buys a crate of $400$ juice boxes. If $60\%$ of the crate is mango juice and $40\%$ is orange juice, he calculates $400 \times 0.60 = 240$ mango boxes and $400 \times 0.40 = 160$ orange boxes.

Common Mistake to Avoid

A common mistake is trying to calculate $60\%$ and $40\%$ of the patio area ($100\text{ m}^2$) first. While that method can also work, finding the total number of tiles first keeps your steps simpler and avoids confusion when different tile shapes have different areas!

As long as both tile shapes have the exact same individual area ($0.25\text{ m}^2$), the geometric shape doesn't change how many total tiles are needed to cover the patio.

In short: Divide the total patio area by the single tile area to get 400 total tiles, then multiply by 0.6 and 0.4 to get 240 square tiles and 160 triangular tiles.