# The area of a circle inscribed in an equilateral triangle is 154 square centimeters. What is the perimeter of the triangle? Use pi=22/7 and square root of 3= 1.73.

Perimeter

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Perimeter

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The radius ( r ) of the inscribed circle can be found using the formula ( A = \frac{\sqrt{3}}{4} \times s^2 ), where ( A ) is the area of the equilateral triangle and ( s ) is the length of its side. Then, the perimeter ( P ) of the triangle can be calculated as ( P = 3s ).

Given that ( A = 154 ) square centimeters, and ( A = \pi r^2 ), solve for ( r ). Then, using ( r ), find the side length ( s ) of the equilateral triangle, and finally compute the perimeter ( P ).

[ r = \sqrt{\frac{A}{\pi}} ] [ s = \frac{2r}{\sqrt{3}} ] [ P = 3s ]

Substitute the given values to find ( r ), then use ( r ) to find ( s ), and finally calculate ( P ).

[ r = \sqrt{\frac{154}{\frac{22}{7}}} ] [ s = \frac{2 \times \sqrt{\frac{154}{\frac{22}{7}}}}{1.73} ] [ P = 3 \times \frac{2 \times \sqrt{\frac{154}{\frac{22}{7}}}}{1.73} ]

Evaluate these expressions to find the perimeter ( P ).

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