# The area of a circle inscribed in an equilateral triangle is 154. find the perimeter of the triangle(pi=22/7 root3= 1.73)

2
by ajay2

2014-10-13T11:42:28+05:30
Area of the circle = 154 sq cm

⇒
⇒r = 7 cm

Let the side of the triangle = a cm
So, s =

But the radius of the incircle,   Where Δ = Area of the triangle and s = semi-perimeter

Perimeter of triangle,

Perimeter of triangle = 42(1.73) = 72.66 cm
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.