If the sides of a triangle are in ratio 3: 4: 5 and its perimeter is 36 cm, then its area is:

The sides of a triangle are in the ratio 3:4:5 \text{ and the perimeter is 36  cm.
Let the sides be  3x,, 4x, 5x.
3x + 4x + 5x = 36
​$$12x = 36 \quad \Rightarrow \quad x = 3$$​​
Actual sides:
​$$3x = 9,\quad 4x = 12,\quad 5x = 15$$​​
Since $$9^2 + 12^2 = 15^2,$$​the triangle is right-angled.
Area of the triangle: $$= \frac{1}{2} \times 9 \times 12 = 54$$​ 

Correct answer is (c)