12. The length and the breadth of a conference hall are in the ratio $$ 8: 5 $$ and its perimeter is 234 m . Find the (i) area of the floor of the hall. (ii) number of tiles, each rectangle of size $$ 20 \mathrm{~cm} imes 15 \mathrm{~cm} $$, required for the floor of the hall. (iii) cost of the tiles at the rate of ₹ 1600 per 100 tiles.

Question

12. The length and the breadth of a conference hall are in the ratio $$ 8: 5 $$ and its perimeter is 234 m . Find the (i) area of the floor of the hall. (ii) number of tiles, each rectangle of size $$ 20 \mathrm{~cm} 	imes 15 \mathrm{~cm} $$, required for the floor of the hall. (iii) cost of the tiles at the rate of ₹ 1600 per 100 tiles.

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Let's solve each part of the problem step by step.

### Given:
- **Ratio of length to breadth**: $$ 8 : 5 $$
- **Perimeter of the hall**: 234 meters

### Let:
- Length = $$ 8x $$ meters
- Breadth = $$ 5x $$ meters

### (i) **Area of the Floor of the Hall**

1. **Calculate $$ x $$:**
   $$
   \text{Perimeter} = 2(\text{Length} + \text{Breadth}) = 2(8x + 5x) = 26x = 234 \text{ m}
   $$
   $$
   x = \frac{234}{26} = 9 \text{ m}
   $$

2. **Find Length and Breadth:**
   $$
   \text{Length} = 8x = 8 \times 9 = 72 \text{ m}
   $$
   $$
   \text{Breadth} = 5x = 5 \times 9 = 45 \text{ m}
   $$

3. **Calculate Area:**
   $$
   \text{Area} = \text{Length} \times \text{Breadth} = 72 \times 45 = 3240 \text{ m}²
   $$

**Answer:**  
   (i) The area of the floor of the hall is **3240 m²**.

### (ii) **Number of Tiles Required**

1. **Convert Dimensions to Centimeters:**
   $$
   \text{Length} = 72 \text{ m} = 7200 \text{ cm}
   $$
   $$
   \text{Breadth} = 45 \text{ m} = 4500 \text{ cm}
   $$

2. **Calculate Total Floor Area in cm²:**
   $$
   \text{Total Area} = 7200 \times 4500 = 32,400,000 \text{ cm}²
   $$

3. **Area of One Tile:**
   $$
   20 \text{ cm} \times 15 \text{ cm} = 300 \text{ cm}²
   $$

4. **Number of Tiles Needed:**
   $$
   \text{Number of Tiles} = \frac{32,400,000}{300} = 108,000 \text{ tiles}
   $$

**Answer:**  
   (ii) The number of tiles required is **108,000 tiles**.

### (iii) **Cost of the Tiles**

1. **Cost per 100 Tiles:** ₹1600

2. **Total Number of 100-Tile Sets:**
   $$
   \frac{108,000}{100} = 1,080 \text{ sets}
   $$

3. **Total Cost:**
   $$
   1,080 \times 1600 = 1,728,000 \text{ ₹}
   $$

**Answer:**  
   (iii) The cost of the tiles is **₹1,728,000**.

---

**Summary of Answers:**
1. **Area:** 3240 m²
2. **Number of tiles:** 108 000 tiles
3. **Total cost:** ₹ 1 728 000
- **Area of the floor:** 3240 m² - **Number of tiles needed:** 108,000 tiles - **Total cost of tiles:** ₹1,728,000

The length and the breadth of a conference hall are in the ratio and its perimeter is 234 m . Find the
(i) area of the floor of the hall.
(ii) number of tiles, each rectangle of size , required for the floor of the hall.
(iii) cost of the tiles at the rate of ₹ 1600 per 100 tiles.

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The length and the breadth of a conference hall are in the ratio and its perimeter is 234 m . Find the (i) area of the floor of the hall. (ii) number of tiles, each rectangle of size , required for the floor of the hall. (iii) cost of the tiles at the rate of ₹ 1600 per 100 tiles.