Question

Find the radius of the incircle of a triangle whose sides are 15 , 20 , 25

Answer 1

Given:

The sides of the triangle

a = 15  

b = 20

c = 25

To find:

Here, we need to find the radius of the incircle of triangle.

Solution:

Area of triangle = $\sqrt{s (s-a) (s-b) (s-c)}$

Here, "s" is the semi perimeter.

To find semi perimeter

$s = \frac{(a +b+c)}{2}$

To find inradius

Inradius $= \frac{Area of triangle }{s}$

First, we will find the semi perimeter.

Put a = 15

     b = 20

      c = 25

$s = \frac{(a +b+c)}{2}$

Substitute the values and find the answer

$s = \frac{( 15 + 20+ 25)}{2}$

$s = \frac{60}{2}$

∴ Semi perimeter = 30

Now, we will put the semi perimeter value as "30" and find the area of the triangle.

Area of triangle = $\sqrt{s (s-a) (s-b) (s-c)}$

                          = $\sqrt{30 (30 - 15) (30 - 20) ( 30 - 25)}$

                          [tex]= \sqrt{30(15) (10) (5)}\\ = \sqrt{30 (750)}\\ = \sqrt{22500}\\ = 150[/tex]

∴ Area of triangle = 150 cm²

Now, we will find the inradius.

Inradius $= \frac{Area of triangle }{s}$      

Here, we need to put the values of area of triangle and semicircle and find the inradius.    

             = $\frac{150}{30}$  

             = 5

∴ The radius of the incircle = 5 cm