Question

find the radius of the incircle of a triangle whose sides arc 15,20,25

Answer 1

Answer:

5

Step-by-step explanation:

From the given lengths we find that it is a right angled triangle by pythagoras theorem

⇒$15^2+20^2=25^2$

⇒$225+400=625$

For finding the radius of incircle, we use the formula

Radius of incircle= Area of triangle / semi perimeter of triangle

(Note: Semi perimeter is half the perimeter)

We know that,

Area of triangle$=\frac{1}{2}*15*20=150$

Semi perimeter$=\frac{1}{2}*(15+20+25)=30$

Hence,

Radius of incircle$=\frac{150}{30}=5$

Hope that helps... :)

Answer 2

radius of incircle=?

we know that

radius of incircle=

$area \div semi \: perimeter$

area of triangle=

$\frac{1}{2} \times base \times height$

$\frac{1}{2} \times 20 \times 15$

=150cm²

$semi \: perimeter = \frac{perimeter}{2}$

$= \frac{ a + b + c}{2}$

$\frac{15 + 20 + 25}{2}$

$\frac{60}{2} = 30$

so

radius= 150/30

=5cm

So the radius of incircle= 5cm