A triangle has sides with lengths of 3, 8, and 2. What is the radius of the triangles inscribed circle?

Good luck! Yonas

The radius ( r ) of the inscribed circle in a triangle can be found using the formula:

[ r = \frac{{\text{Area of the triangle}}}{{\text{Semiperimeter of the triangle}}} ]

where the semiperimeter ( s ) of the triangle is calculated as:

[ s = \frac{{a + b + c}}{2} ]

and ( a ), ( b ), and ( c ) are the lengths of the sides of the triangle.

Given the lengths of the sides of the triangle as ( a = 3 ), ( b = 8 ), and ( c = 2 ), we first need to calculate the semiperimeter ( s ). Then, we use the formula for the area of a triangle, which can be calculated using Heron's formula:

[ \text{Area} = \sqrt{s(s - a)(s - b)(s - c)} ]

Finally, we substitute the values of the area and semiperimeter into the formula for the radius of the inscribed circle.

After computing these values, we find the radius of the inscribed circle of the triangle.