Question

The lengths of the sides of a triangle are in ratio 3:4:5. Find the area of the triangle if its perimeter is 144cm

Answer 1

Solution:

Given the perimeter of a triangle is 160m and the sides are in a ratio of 3 : 4 : 5

Let the sides a, b, c of a triangle be 3x, 4x, 5x respectively

So, the perimeter = 2s = a + b + c

144 = a + b + c

144 = 3x+ 4x+ 5x

Therefore, x = 12cm

So, the respective sides are

a = 36cm

b = 48cm

c = 60cm

Now, semi perimeter s = (a+b+c)/2

= (36+48+60)/2

= 72 cm

By using Heron’s Formula

The area of a triangle = √s×(s−a)×(s−b)×(s−c)

= √72×(72−36)×(72−48)×(72−60)

= 864cm2

Thus, the area of a triangle is 864cm2