Question

If the perimeter of a triangle is 36 cm. Its inner radius is 4.5 cm. Is. Find its area.​

Answer 1

Step-by-step explanation:

Given;-

perimeter=36

let the ratio be x

therefore,

⇒AB+BC+CA=36

⇒3x+4x+5x=36

⇒12x=36

⇒x=

12

36

⇒x=3

Now, putting the value of x

AB=3x=9cm

BC=4x=12cm

AC=5x=15cm

On using Pythagoras theorem

AC

2

=AB

2

+BC

2

=(9)

2

+(12)

2

=81+144

AC

2

=225

AC=15cm

ΔABC is right angled triangle ∠B is right angle.

Area of

ΔABC=

2

1

AB×BC

=

2

1

×9×12

=54cm

2

hence,

Area of triangle is 54cm

2