Question

Сторона равностороннего треугольника равна 12 корень из 3 найдите его медиану?

Answer 1

Формула L(биссектрисы, высоты и медианы) в равностороннем треугольнике $L= \frac{ a\sqrt{3} }{2}$
$L= \frac{12* \sqrt{3}* \sqrt{3} }{2} = \frac{12*3}{2}=18$
Ответ=18

Answer 2

Finding the Median of an Equilateral Triangle

To find the median of an equilateral triangle, we first need to understand what a median is. In geometry, a median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. In an equilateral triangle, all three medians are the same length and intersect at a point called the centroid.

Given that the side length of the equilateral triangle is 12√3, we can find the length of the median using the following steps:

1. Find the height of the equilateral triangle (h): - The height of an equilateral triangle can be calculated using the formula h = (√3/2) * a, where a is the length of one side of the triangle. - Substituting the given side length of 12√3 into the formula, we get h = (√3/2) * 12√3. - Simplifying the expression, h = 6 * 3 = 18.

2. Calculate the length of the median (m): - The length of the median can be found using the formula m = (1/2) * √(2b^2 + 2c^2 - a^2), where a, b, and c are the side lengths of the triangle. - Since the triangle is equilateral, all three side lengths are the same, so a = b = c = 12√3. - Substituting the values into the formula, we get m = (1/2) * √(2(12√3)^2 + 2(12√3)^2 - (12√3)^2). - Simplifying the expression, m = (1/2) * √(288 + 288 - 432). - Further simplifying, m = (1/2) * √(144). - Taking the square root, m = (1/2) * 12 = 6.

Therefore, the median of the equilateral triangle with a side length of 12√3 is 6.