The ratio of the length to the breadth of a rectangular park is $3 : 2$, and its perimeter is 120m. What is the area of the park in square meters?

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**Solution:**

1. Let the length of the park be $3x$ and the breadth be $2x$ according to the given ratio $3 : 2$.

2. The perimeter $P$ of a rectangle is given by:
   $$P = 2(L + B)$$
   Substituting the values:
   $$120 = 2(3x + 2x) = 2(5x) = 10x$$

3. Solve for $x$:
   $$x = \frac{120}{10} = 12$$

4. Calculate the length and breadth:
   - Length $L = 3x = 3 	imes 12 = 36 	ext{ m}$
   - Breadth $B = 2x = 2 	imes 12 = 24 	ext{ m}$

5. Find the area $A$ of the rectangle:
   $$A = L 	imes B = 36 	imes 24 = 864 	ext{ m}^2$$

**Answer:** $864$

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