Question

Знайдіть радіус кола, вписаного в рівносторонній трикутник, якщо висота трикутника 36 см.

Answer 1

Пусть сторона треугольника равна x, тогда

x^2-(x/2)^2=36^2

3x^2=5184

x^2=1728

x=24*sqrt(3)

Радиус определим по формуле

r=A*sqrt(3)/6

В нашем случае  r=24*sqrt(3)*sqrt(3)/6=12

Answer 2

Finding the Radius of the Inscribed Circle in an Equilateral Triangle

To find the radius of the circle inscribed in an equilateral triangle, we can use the formula:

Radius of inscribed circle = (Height of the equilateral triangle) / 2

Given that the height of the equilateral triangle is 36 cm, we can calculate the radius of the inscribed circle as follows:

Radius of inscribed circle = 36 cm / 2 = 18 cm

Therefore, the radius of the circle inscribed in the equilateral triangle is 18 cm.