The ratio between the length and the breadth of a rectangular park is $3 : 2$, and the perimeter of the park is $120 ext{ m}$. Find the area (in $ ext{m}^2$) of the park.

Question

The ratio between the length and the breadth of a rectangular park is $3 : 2$, and the perimeter of the park is $120 	ext{ m}$. Find the area (in $	ext{m}^2$) of the park.

Accepted Answer

**Solution:**

1. Let the length be $3x$ and the breadth be $2x$.

2. Given perimeter $P = 120 	ext{ m}$.

3. Perimeter of rectangle formula:
   $$P = 2(l + b) = 2(3x + 2x) = 2 	imes 5x = 10x$$

4. Equate and solve for $x$:
   $$10x = 120 \implies x = \frac{120}{10} = 12$$

5. Calculate length and breadth:
   - Length $l = 3x = 3 	imes 12 = 36 	ext{ m}$
   - Breadth $b = 2x = 2 	imes 12 = 24 	ext{ m}$

6. Calculate area $A$:
   $$A = l 	imes b = 36 	imes 24 = 864 	ext{ m}^2$$

**Answer:** $864 	ext{ m}^2$

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