Calculate the perimeter of an equilateral triangle if it inscribes a circle whose area is 154 cm2
Answers
make my answer as brainalist.
Area of the circle = 154 sq cm
⇒\pi r^2 = 154πr
2
=154
⇒ \frac{22}{7} r^2 = 154
7
22
r
2
=154
⇒ r^2 = 49r
2
=49
⇒r = 7 cm
Let the side of the triangle = a cm
So, s = \frac{3a}{2}
2
3a
But the radius of the incircle, r = \frac{\Delta}{s} r=
s
Δ
Where Δ = Area of the triangle and s = semi-perimeter
7 = \frac{ \frac{ \sqrt{3} }{4} a^2 }{ \frac{3a}{2} } 7=
2
3a
4
3
a
2
7 = \frac{ \sqrt{3}a^2 }{2*3a} 7=
2∗3a
3
a
2
7 = \frac{ \sqrt{3}a}{6} 7=
6
3
a
But the radius of the incircle, r = \frac{\Delta}{s} r=
s
Δ
Where Δ = Area of the triangle and s = semi-perimeter
7 = \frac{ \frac{ \sqrt{3} }{4} a^2 }{ \frac{3a}{2} } 7=
2
3a
4
3
a
2
7 = \frac{ \sqrt{3}a^2 }{2*3a} 7=
2∗3a
3
a
2
7 = \frac{ \sqrt{3}a}{6} 7=
6
3
a
Answer:
Answer is 72.66
Hope it helps u ☺☺
