Question

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

Answer 1

Let the sides of the triangle are

a = 3x

b = 4x

c = 5x

Given that the perimeter is 144 cm.

Hence

3x + 4x + 5x = 144

⇒ 12x = 144

⇒ x = `144/12`

⇒ x = 12

s = `(a + b + c)/(2)`

= `(12x)/(2)`

= 6x

= 6 × 12

= 72

The sides are a = 36 cm, b = 48 cm and c = 60 cm.

Area of the triangle is

A = `sqrt (s(s - a )( s - b ) (s - c ))`

= `sqrt (72(72 - 36 )( 72 - 48 ) (72 - 60))`

= `sqrt (72 xx 36 xx 24 xx 12)`

= `sqrt746496`

= 864 cm²