Question

the area of a circle inscribed in a equilateral triangle is 154cm sq find the perimeter of triangle

Answer 1

Answer:

Step-by-step explanation:

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.

Answer 2

Sol: Given area of inscribed circle = 154 sq cmLet the radius of the incircle be r. ⇒ Area of this circle = πr2 = 154 (22/7) × r2 = 154⇒ r2 = 154 × (7/22) = 49 ∴ r = 7 cm Recall that incentre of a circle is the point of intersection of the angular bisectors.Given ABC is an equilateral triangle and AD = h be the altitude. Hence these bisectors are also the altitudes and medians whose point of intersection divides the medians in the ratio 2 : 1∠ADB = 90° and OD = (1/3) AD That is r = (h/3) Þ h = 3r = 3 × 7 = 21 cm Let each side of the triangle be a, then Altitude of an equilateral triangle is (√3/2) times its side That is h = (√3a/2) ∴ a = 14√3 cm We know that perimeter of an equilateral triangle = 3a = 3 × 14 √3 = 42√3 = 42 × 1.73 = 72.66 cm