Question

If the sides of a right-angled triangle are in ratio 3 : 4 : 5, and its perimeter is 48 cm, then its area (in $c{m}^2$) is ___.

• A. 30
• B. 45
• C. 96
• D. 135

Answer 1

The correct option is C 96

Let the sides of the triangle be 3y, 4y and 5y.
Given: Perimeter = 48 cm
Hence, 3y + 4y + 5y = 48
⇒ 12y = 48
⇒ y = 4
Thus, the measure of the sides are 12 cm, 16 cm, and 20 cm.
Also, the sides of length 12 cm and 16 cm are the perpendicular sides, while the side of length 20 cm is the hypotenuse.

So, the area of the right-angled triangle
= $\frac{1}{2}$ $\times$ (Product of perpendicular sides)
= $\frac{1}{2}$ $\times$ (12 $\times$ 16) = 96 $c{m}^2$