Question

5. The area of incircle of an equilateral triangle is 154 cm². The perimeter of the
triangle is
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Answer 1

Given Area of circle=154cm ^2

⇒πr ^2  =154cm^2⇒r^2 = 154*7/22 =49cm

⇒r=  49/7

​ =7cm

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

0 is the in center 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=  1/3  AD & OD is radius of circle. Then,

r= h/3  ⇒h=3r=3×7=21cm

Let each side of an equilateral triangle be 'a', then altitude of an equilateral triangle is ( 3/2) times its side. So that

h=3/2   a⇒a= 2h/3   = 2*21/3=2*21*3/3 =14  divided 3  cm

Perimeter of triangle ABC=3a=3×14  

42 rays to 3 cm

=42×1.73

=72.66cm^2

The perimeter of the

triangle is =72.66cm^2

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