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ICSE Class 10 Answered

the area of a circle insribed in an equilateral triangle is 154sq.cm, find the perimeter of triangle

Asked by subhasray1968 | 09 Feb, 2018, 12:27: PM
Expert Answer

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

Answered by | 09 Feb, 2018, 01:48: PM
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