Question

Медиана равностороннего треугольника равна 11 корень из 3. Найдите его сторону. подробно

Answer 1

Каждый угол равностороннего треугольника равен 60 градусов .Раздели высоту(медиану) на синус 60 градусов. Получается=11корень из 3: корень 3 из 2. Ответ 11корень из 3 делить на корень 3 из 2

Answer 2

Медиана в равностор треуг-ке делит его сторону пополам и так же образует с ней прямой угол
пусть треуг-к АВС, медиана ВО
рассмотрим тр-к АВО, прямоуг
по теореме пифагора:
АВ^2=ВО^2+АО^2
обозначим сторону за х, т.е. АВ=х, тогда АО= 1/2х, так как сторона пополам медианой поделилась
получаем:
х^2=(11√3)^2+(1/2х)^2
3/4х^2=363
х^2=121*4
х=√121*4=11*2=2

Answer 3

Finding the Side Length of an Equilateral Triangle with a Median of 11√3

To find the side length of an equilateral triangle with a median of 11√3, we can use the properties of equilateral triangles.

An equilateral triangle is a triangle with all three sides of equal length. The median of an equilateral triangle is a line segment that connects one vertex to the midpoint of the opposite side. In an equilateral triangle, the median is also an altitude and a perpendicular bisector of the opposite side.

Let's denote the side length of the equilateral triangle as s.

To find the side length, we can use the relationship between the side length and the median of an equilateral triangle. The median of an equilateral triangle is equal to half the side length multiplied by the square root of 3.

Therefore, we have the equation:

11√3 = (s/2)√3

To solve for s, we can cancel out the square root of 3 on both sides of the equation:

11 = s/2

Multiplying both sides of the equation by 2, we get:

22 = s

Therefore, the side length of the equilateral triangle is 22.

Please let me know if I can help you with anything else.