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

Answer:

The radius of the circle is 14.4 cm.

Step-by-step explanation:

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

The area of a triangle is given by

$A=\frac{1}{2}\cdot a\cdot h\\\\270.633=\frac{1}{2}\cdot a\cdot 21.65\\\\a=25.0007$

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

$BD=\frac{a}{2}\\\\BD=\frac{25.0007}{2}\\\\BD=12.50035$

Hence, in triangle OBD, we have

$\cos30^{\circ}=\frac{BD}{r}\\\\\frac{\sqrt3}{2}=\frac{12.50035}{r}\\\\r=14.4$

The radius of the circle is 14.4 cm.

Answer 2

The answer will be 14.4cm