Question

A right triangle has sides 8 cm, 15 cm and 17 cm. Find the radius of the inscribed circle as well as the area of circle.

Answer 1

Step-by-step explanation:

In ∆ABC , AB=8cm ,BC=15 cm. and AC=17cm.

AB^2+BC^2=8^2+15^2= 64+225=289.

And. AC^2= 17^2=289.

Here , AB^2+BC^2= AC^2 , ∆ABC is a right angled triangle at Point B .

Area of the ∆ABC= (1/2)×8×15 = 60cm^2.

Radius of in circle (r) = area of∆ABC/semi perimeter of ∆ABC.

r = 60 cm^2/{(8+15+17)/2 } cm = 60/20 cm =3 cm

Area=πr^2=22/7*3*3=198/7=28.29 cm^2

Hope it helps