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

r = 14.4

Explanation:

Answer 2

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