Question

What radius of a circle is required to inscribe an equilateral triangle with an area of 270.633 cm2 and an altitude of 21.65 cm? (round to nearest tenth)

Answer 1

The answer will be 14.4cm

Answer 2

The radius of the circle is 14.4 cm.

Explanation:

Let a be the side of the equilateral triangle and r be the radius.

The area of a triangle is given by

`A=(1)/(2)\cdot a\cdot h\\\\270.633=(1)/(2)\cdot a\cdot 21.65\\\\a=25.0007`

We have calculate the side of the triangle. From the figure,

`BD=(a)/(2)\\\\BD=(25.0007)/(2)\\\\BD=12.50035`

Hence, in triangle OBD, we have

`\cos30^(\circ)=(BD)/(r)\\\\(\sqrt3)/(2)=(12.50035)/(r)\\\\r=14.4`

The radius of the circle is 14.4 cm.