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2014-10-13T11:42:28+05:30
Area of the circle = 154 sq cm
\pi r^2 = 154
 \frac{22}{7} r^2 = 154
 ⇒ r^2 = 49
⇒r = 7 cm

Let the side of the triangle = a cm
So, s =  \frac{3a}{2}

But the radius of the incircle, r = \frac{\Delta}{s}  Where Δ = Area of the triangle and s = semi-perimeter

7 =  \frac{ \frac{ \sqrt{3} }{4} a^2 }{ \frac{3a}{2} }

7 =  \frac{ \sqrt{3}a^2 }{2*3a}

7 =  \frac{ \sqrt{3}a}{6}

a =  \frac{42}{ \sqrt{3} }

a = \frac{42 \sqrt{3}}{3 } = 14 \sqrt{3}

Perimeter of triangle, 3a = 3*14 \sqrt{3} = 42 \sqrt{3}

Perimeter of triangle = 42(1.73) = 72.66 cm 
1 5 1
good job
The process was Rationalisation of root 3...I multiplied and divided by root 3
short cut
no it is conjucate multiply of root 3 in denominator and in numerator
Its not conjugate....its rationalising factor
2014-10-13T18:51:21+05:30
The area of the circle=154 cm²
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 cm.

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