Question

find the perimeter of an equilateral triangle if it inscribes a circle whose area is 110cm²​

Answer 1

let the side of equilateral triangle be 'a'.

area of equilateral triangle =

$\frac{ \sqrt{3} {a}^{2} }{4}$

area of equilateral triangle = 110 sq.cm.

$\frac{ \sqrt{3} {a}^{2} }{4} = 110$

$\sqrt{3} {a}^{2} = 110 \times 4$

${a}^{2} = \frac{440}{ \sqrt{3} }$

$a = \sqrt{ \frac{440}{ \sqrt{3} } } = 16(approx)$

therefore, side of the equilateral triangle is 16 cm.