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)

To solve this problem you must apply the proccedure shown below:

1. You must apply the formula for calculate the area of a equilateral triangle and clear the side of the triangle (s):

A = (√3) s²/4

s²=4A/√3

s² = (4x270.633 cm²) / 4

s²=625 cm²

s=√625 cm²

s=25 cm

2. Now, you can find the radius (r) of the circle by applying the following formula:

r=s/√3

s is the side of the triangle

3. Therefore, you have:

r=25 cm/√3

r=14.43 cm

4. As you can see, the answer is:

r=14.43 cm