Question

Find the area of a triangle whose sides are in the ratio of 5:12:13 and its perimeter is 60 cm.

Answer 1

5x + 12x + 13x =60

30x = 60

X =3/6

X = 2

First side 10cm

Second side 24cm

Third side 26cm

Answer 2

Let the sides be 5x, 12x and 13x.

Perimeter = 60 cm (Given)

Also, Perimeter = Sum of all sides

•°• Sum of all sides = 60 cm

5x + 12x + 13x = 60

30x = 60

x = 60 / 30

x = 2

Sides are :

First side = 5x = 5 ( 2 ) = 10 cm

Second side = 12x = 12 ( 2 ) = 24 cm

Third side = 13x = 13 ( 2 ) = 26 cm

Applying Heron's Formula :

s = ( a + b + c ) / 2

Here, a, b and c are the sides of Triangle.

s = ( 10 + 24 + 26 ) / 2 = 60 / 2 = 30

Now,

Area of Triangle = √ s ( s - a ) ( s - b ) ( s - c )

= √ 30 ( 30 - 10 ) ( 30 - 24 ) ( 30 - 26 )

= √ 30 ( 20 ) ( 6 ) ( 4 )

= √ 2 × 2 × 2 × 2 × 3 × 3 × 10 × 10

= 10 × 2 × 2 × 3

= 120 cm²

Hence, the area of triangle is 120 cm².