Question

In a right angled triangle ABC, angle B = 90°. If AB= 8, BC = 15,find the perimeter of ∆ ABC​

Answer 1

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In a right triangle ABC, right angled at B, BC=15cm, and AB=8cm. A circle is inscribed in triangle ABC. The radius of the circle is :

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ANSWER

Using Pythagoras theorem in △ABC

(AB)

2

+(BC)

2

=(AC)

2

(15)

2

+(8)

2

=(AC)

2

⇒(AC)

2

=225+64=289

⇒AC=17cm

Now inradius r=

s

Δ

where Δ is the area of triangle and s is semi perimeter.

Δ=

2

1

×8×15=60

s=

2

8+15+17

=

2

40

=20

⇒r=

s

Δ

=

20

60

=3cm