Find the radius of a circle circumscribed about a triangle whose sides are 5m, 4m, 3m.

From the condition it is known that we are given a triangle with side lengths of 5 m, 4 m and 3 m. It is also known that a circle is described around the triangle.

In order to find the radius of the circumscribed circle, we first define the type of triangle.

Let’s use the Pythagorean theorem:

5 ^ 2 = 3 ^ 2 + 4 ^ 2;

25 = 25,

we conclude that the triangle is rectangular.

Recall the formula for the radius of a circle circumscribed about a right-angled triangle.

R = 1 / 2√ (a ^ 2 + b ^ 2),

Where a and b are the legs of the triangle.

R = 1 / 2√ (4 ^ 2 + 3 ^ 2) = 1 / 2√25 = 1/2 * 5 = 2.5 m.