Question

if the length of the sides of a triangle are in ratio 3:4:5 and its perimeter is 48 cm ,find its area

Answer 1

The solution is very simple.

Solution:
The perimeter of the triangle = 48 cm
The length of the sides are in ratio = 3:4:5
The sum of the ratio's = 3+4+5 = 12
So, the length of the 1st side = (3/12 * 48)cm = 12 cm
Length of the second side = (4/12 * 48)cm = 16 cm
Length of the third side = (5/12 * 48)cm = 20 cm

The lengths of three sides are 12cm, 16cm, and 20cm respectively.

Then use the Hero's formula = $\sqrt{s(s-a)(s-b)(s-c)}$,  where s = a + b + c / 2,  where a = 12 cm, b = 16 cm, and c = 20 cm

So, the area of the triangle = $\sqrt{24cm(24cm-12cm)(24cm-16cm)(24cm-20cm)}$ = $\sqrt{24cm * 12cm * 8cm * 4cm}$ = 96cm²

Ans : The area of the triangle is 96 cm².