Question

Calculate the perimeer of an equileral triangle if it inscribes a circle whos ara is 154 cm2​

Answer 1

$\huge\underline\mathrm{Question}:-$

Calculate the perimeter of an equilateral triangle if it inscribes a circle whose area is 154 cm².

$\huge\underline\mathrm{Solution}:-$

Here, as the equilateral triangle inscribed in a circle, the circle is an incircle.

Now, the radius of the incircle is given by,

r = Area of triangle/semi-perimeter

In the question, it is given that area of the incircle = 154 cm²

So, π × r² = 154

Or, r = 7 cm

Now, assume the length of each arm of the equilateral triangle to be “x” cm

So, the semi-perimeter of the equilateral triangle = (3x/2) cm

And, the area of the equilateral triangle = (√3/4) × x²

We know, r = Area of triangle/semi-perimeter

So, r = [x2(√3/4)/ (3x/2)]

=> 7 = √3x/6

Or, x = 42/√3

Multiply both numerator and denominator by √3

So, x = 42√3/3 = 14√3 cm

Now, the perimeter of an equilateral triangle will be = 3x = 3 × 14√3 = 72.7 cm.