Question

Гипотенуза равнобедренного прямоугольного треугольника равна 12 см. Найдите длину медианы, проведенной к гипотенузе

Answer 1

Медиана в прямоугольном треугольнике, проведенная к гипотенузе, равна половине гипотенузы. Т. е. 6 см

Answer 2

Finding the Length of the Median

To find the length of the median drawn to the hypotenuse of an isosceles right triangle with a hypotenuse of 12 cm, we can use the properties of isosceles triangles.

In an isosceles right triangle, the median drawn to the hypotenuse is also the altitude and the angle bisector. This means that it divides the triangle into two congruent right triangles.

Let's denote the length of the median as 'm'. Since the median divides the hypotenuse into two equal parts, each part will have a length of 'm'. Therefore, we can write the following equation:

2m + m = 12

Simplifying the equation, we get:

3m = 12

Dividing both sides by 3, we find:

m = 4

Therefore, the length of the median drawn to the hypotenuse of the isosceles right triangle is 4 cm.