Question

4. The area of a circle inscribed in an equilateral triangle is 154 cm? Find the perimeter of
triangle​

Answer 1

Answer:

the perimeter of the triangle will be half into base into height

Answer 2

Given Area of circle=154cm²

⇒πr²=154cm²⇒r² = 154×7/22=49cm

$r = \sqrt{49} = 7cm$

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=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√3cm

Perimeter of triangle ABC=3a=3×14√3cm=42√3 cm=42×1.73

=72.66cm²