The area of a right-angled triangle is 54 sq. cm. One of its legs has length 12 cm. Find its perimeter.

Given, $\text{Area} = 54 \text{ cm}^2$

$$\text{Leg}_1 = 12 \text{ cm}$$

$$\text{Area}=\frac{1}{2}\times\text{Leg}_1\times\text{Leg}_2$$

$$54=\frac{1}{2}\times12\times\text{Leg}_2$$

$$\text{Leg}_2 = 9 \text{ cm}$$

$$\text{Hypotenuse} = \sqrt{12^2 + 9^2}$$

$$= \sqrt{144 + 81}$$

$$= \sqrt{225}$$

$$= 15 \text{ cm}$$

$$\text{Perimeter} = 12 + 9 + 15$$

$$= 36 \text{ cm}$$