Question

The area of a circle inscribed in an equilateral triangle is 154 cm². Find the perimeter of the triangle. [Use $(\pi=\frac{22}{7})$ and 3 = 1.73]

Answer 1

Answer:

Perimeter of equilateral triangle is 72.7 cm²

Step-by-step explanation:

SOLUTION :  

Given :  

Area of inscribed circle = 154 cm²

Area of circle = πr²

Area of inscribed circle = 154 cm²

πr² = 154 cm²

r² = 154/π

r² = (154 × 7)/22

r² = 7 × 7  

r = √7 × 7

r = 7 cm

Radius of inscribed circle = 7cm

Let a be  side of an equilateral triangle

We know that, radius of incircle ,r = side/2√3

r = a/2√3

7 = a/2√3

a = 7 × 2√3  

a = 14√3

Side of an equilateral triangle,a = 14√3 cm

 

Perimeter of equilateral triangle = 3 × side = 3 × a  

= 3 × 14√3

= 42 × 1.73  

[Given √3 = 1.73]

= 72.66 = 72.7 cm²

Hence,Perimeter of equilateral triangle is 72.7 cm²

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Answer 2

therefore, πr²=154 cm²

or,22r²/7=154 cm²

or,r²=154 cm²*7/22=49 cm²

or,r=7 cm.

Let the side of the triangle be x cm.

Therefore, semi perimeter=3x/2

Radius of the circle=Area/Semi Perimeter of Δ.

or,7=(√3/4*x²)/(3x/2)

or,7=(√3*x)(3*2)

or,7=(√3*x)/6

or,7*6=√3*x

or,42=√3*x

or,42/√3=x

or,x=42/√3

Perimeter=42*/√3*3=42√3=42*1.73=72.66