Find the radius of a circle circumscribed about a triangle with sides 5 m, 6 m, 7 m.

As we know from the school mathematics course, the radius of the circumscribed circle can be calculated using the following formula:

R = abc / 4S.

Let’s determine what the half-perimeter of this triangle will be:

(5 + 6 + 7): 2 = 18: 2 = 9.

Determine what the area of the triangle of this triangle will be equal to:

√ (9 * (9 – 5) * (9 – 6) * (9 – 7)) = √ (9 * 4 * 3 * 2) = 6√6.

Let us determine what the radius of the circumscribed circle will be equal to in our case:

R = (5 * 6 * 7) / (4 * 6√6) = 35 / 4√6.

Answer: Radius = 35 / 4√6 m.