Question

. The area of incircle of an equilateral triangle is 154 cm? The perimeter of the triangle .
​

Answer 1

Answer:

Given Area of circle=154cm

2

⇒πr

2

=154cm

2

⇒r

2

=

22

154×7

=49cm

⇒r=

49

=7cm

ABC is an equilateral △, h is the altitude of △ABC

0 is the incenter of △ABC, and this is the point of intersection of the angular bisectors. Hence, these bisectors are also the altitude and medians whose point of intersection divides the medians in the ratio 2:1

∴∠ADB=90° & OD=

3

1

AD & OD is radius of circle. Then,

r=

3

h

⇒h=3r=3×7=21cm

Let each side of an equilateral triangle be 'a', then altitude of an equilateral triangle is (

2

3

) times its side. So that

h=

2

3

a⇒a=

3

2h

=

3

2×21

=

3

2×21

3

=14

3

cm

Perimeter of triangle ABC=3a=3×14

3

cm=42

3

cm=42×1.73

=72.66cm

2