The base of the isosceles triangle is 12, and the height is 3. Find the diameter of the circumscribed

| May 13, 2021 | education

The base of the isosceles triangle is 12, and the height is 3. Find the diameter of the circumscribed circle around this triangular.

First, let’s find the length of the lateral side of this isosceles triangle.

Consider one of the triangles by which the height lowered to the base divides this isosceles triangle.

This triangle is right-angled, one of its legs is the height lowered to the base, the second leg is half the base of this isosceles triangle, and the hypotenuse is the lateral side of this isosceles triangle.

Using the Pythagorean theorem, we find the length of the lateral side:

√ (3 ^ 2 + (12/2) ^ 2) = √ (3 ^ 2 + 6 ^ 2) = √ (9 + 36) = √45 = 3√5.

Find the area S of a given isosceles triangle:

S = 3 * 12/2 = 3 * 6 = 18.

Using the formula for the area of ​​a triangle through the radius R of the circumscribed circle, we find R:

R = (12 * 3√5 * 3√5) / (4 * 18) = 12 * 45/72 = 540/72 = 7.5.

Answer: 7.5.



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