Given :

Ratio of sides of the triangle = 5 : 4 : 3

Perimeter of thetriangle = 36 cm

To Find :

The area of the triangle using heron's formula

Solution :

Let the ratio constant be " x " . Then sides of the triangle are 5x , 4x and 3x.

Perimeter of a triangle is given by ,

Here ,

a , b and c are sides of triangle

Substituting the values we have in the formula ,

Then , Sides of the given triangle are ;

5x = 5(3) = 15 cm

4x = 4(3) = 12 cm

3x = 3(3) = 9 cm

Now , Area of triangle (heron's formula) is given by ;

Here ,

s is semiperimeter

a , b and c are sides of triangle

Now , Calculating the semiperimeter of given triangle ;

Substituting the values we have in the heron's formula ;

Hence ,

Given :-

*Perimeter of triangle = 36 cm

*Ratio of their sides 5:4:3

To Find :-

Area of triangle

Solution :-

As we know that Perimeter is sum of all sides  

Let the sides be 5x , 4x and 3x

36 = 5x + 4x + 3x

36 = 12x

x = 3

Sides are

5x = 5*3 = 15 cm

4x = 4*3 = 12 cm

3x = 3*3 = 9 cm

Now,

Let's find Semiperimeter by using Herons formula,

Semiperimeter = Perimeter / 2

Semiperimeter = 36/2 = 18

Now,

Let's use Herons formula

⚡HOPE IT HELPS YOU⚡