Question

Если треугольник периметр которого равен 15 см делится медианой на два треугольника с периметрами 11см и 14 см то длина медианы равна

Answer 1

Пусть медиана равна $m$,  стороны пусть равны $a,b,c$
$P=a+b+c=15\\ P_{1}=0.5a+b+m=11\\ P_{2}=0.5a+c+m=14\\ \\ a+2b+2m=22\\ a+2c+2m=28\\ \\ a+b+c=15\\ 2a+2(b+c)+4m=50\\ 2a+30-2a+4m=50\\ 4m=20\\ m=5$
Равна 5 

Answer 2

Calculating the Median Length of a Triangle

To calculate the length of the median of a triangle, we can use the fact that the medians of a triangle divide each other in a 2:1 ratio. Given that the perimeter of the triangle is 15 cm and it divides the median into two triangles with perimeters of 11 cm and 14 cm, we can calculate the length of the median.

Let's denote the length of the median as m.

Solution

We know that the perimeter of the original triangle is 15 cm, and it divides the median into two triangles with perimeters of 11 cm and 14 cm.

Using the property that the medians of a triangle divide each other in a 2:1 ratio, we can set up the following equation:

2x + x = 15

Where: - x is the length of the median.

Solving for x: 3x = 15 x = 5

So, the length of the median (m) is 5 cm.

This calculation is based on the property of medians in a triangle and the given information about the perimeters of the divided triangles.