The length and breadth of a rectangle are in the ratio $4:7$. If the perimeter of the rectangle is $88 ext{ cm}$, find the area of the rectangle.

Question

The length and breadth of a rectangle are in the ratio $4:7$. If the perimeter of the rectangle is $88 	ext{ cm}$, find the area of the rectangle.

Accepted Answer

**Solution:**

1. Let the length and breadth of the rectangle be $4x$ cm and $7x$ cm respectively.

2. The perimeter of a rectangle is given by:
   $$	ext{Perimeter} = 2(	ext{length} + 	ext{breadth})$$

3. Substitute the values:
   $$2(4x + 7x) = 88$$
   $$2(11x) = 88$$
   $$22x = 88$$
   $$x = \frac{88}{22} = 4$$

4. Calculate the area:
   $$	ext{Area} = 	ext{length} 	imes 	ext{breadth} = 4x 	imes 7x = 28x^2$$
   $$= 28 	imes 4^2 = 28 	imes 16 = 448 	ext{ cm}^2$$

**Answer:** $448 	ext{ cm}^2$

Answer

Answer

Answer