Question

R круга вписанного в правильный треугольник равно 2 корней из 3 см.Найдите периметр треугольника

Answer 1

Радиус вписанной окружности (r) в правильного треугольника равен $\frac{a}{ 2\sqrt{3} }$, где a - сторона треугольника. ⇒ a=r*$2\sqrt{3}$ = $2\sqrt{3} * 2\sqrt{3} =12$
P=3a=3*12=36 (см)
Ответ: 36 см.

Answer 2

Perimeter of a Triangle Inscribed in a Regular Triangle

To find the perimeter of a triangle inscribed in a regular triangle, we need to determine the side length of the regular triangle.

Given that the radius of the inscribed circle is equal to 2√3 cm, we can use the relationship between the radius of the inscribed circle and the side length of the regular triangle.

According to the formula for the radius of the inscribed circle in a regular triangle, R = (a√3)/6, where R is the radius of the inscribed circle and a is the side length of the regular triangle.

By rearranging the formula, we can solve for the side length of the regular triangle:

a = (6R)/√3

Substituting the given radius value, we have:

a = (6 * 2√3)/√3 = 12 cm

Therefore, the side length of the regular triangle is 12 cm.

To find the perimeter of the triangle, we simply multiply the side length by 3:

Perimeter = 3 * 12 cm = 36 cm

So, the perimeter of the triangle inscribed in the regular triangle is 36 cm.

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