The breadth and length of a larger rectangle are $93 ext{ cm}$ and $152 ext{ cm}$ respectively. If the breadth of a smaller rectangle is $\frac{1}{3}$ of the breadth of the larger rectangle and the length of the smaller rectangle is $\frac{1}{4}$ of the length of the larger rectangle, what is the area of the smaller rectangle?

Question

The breadth and length of a larger rectangle are $93 	ext{ cm}$ and $152 	ext{ cm}$ respectively. If the breadth of a smaller rectangle is $\frac{1}{3}$ of the breadth of the larger rectangle and the length of the smaller rectangle is $\frac{1}{4}$ of the length of the larger rectangle, what is the area of the smaller rectangle?

Accepted Answer

**Solution:**

1. Given the dimensions of the larger rectangle:
   - Breadth = $93 	ext{ cm}$
   - Length = $152 	ext{ cm}$

2. The smaller rectangle's breadth is $\frac{1}{3}$ of the larger rectangle's breadth:
   $$	ext{Breadth}_{small} = \frac{1}{3} 	imes 93 = 31 	ext{ cm}$$

3. The smaller rectangle's length is $\frac{1}{4}$ of the larger rectangle's length:
   $$	ext{Length}_{small} = \frac{1}{4} 	imes 152 = 38 	ext{ cm}$$

4. Calculate the area of the smaller rectangle:
   $$	ext{Area}_{small} = 	ext{Length}_{small} 	imes 	ext{Breadth}_{small} = 38 	imes 31 = 1178 	ext{ cm}^2$$

**Answer:** $1178 	ext{ cm}^2$

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