ABC26GN4641 · Area
Subject: General Aptitude · Chapter: Area · Exam: 2006 · Marks: · Difficulty:
The area of a circle inscribed in an equilateral triangle is $154 \mathrm{cm}^{2}$. Find the perimeter of the triangle.
(a)71.5 cm
(b)71.7 cm
(c)72.3 cm
(d)72.7 cm
Answer
Explanation
Radius of incircle $=\frac{a}{2 \sqrt{3}}$. Area of incircle $=\left(\frac{\pi \times a^{2}}{12}\right) \mathrm{cm}^{2}$. $\therefore \quad \frac{\pi a^{2}}{12}=154 \Leftrightarrow a^{2}=\frac{154 \times 12 \times 7}{22} \Leftrightarrow a=14 \sqrt{3}$. ∴ Perimeter of the triangle $=(3 \times 14 \sqrt{3}) \mathrm{cm}$ $=(42 \times 1.732) \mathrm{cm}=72.7 \mathrm{cm}$ (approx.)
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