Question

СРОЧНО З ПОЯСНЕННЯМ! Периметр трикутника дорівнює 23 см. Медіана ділить даний трикутник на два трикутники, периметри яких дорівнюють 18 см і 17 см. Знайдіть довжину медіани.

Answer 1

Ответ:

медіана=6см

АВС- трикутник ВМ-медіана

АС=АМ+МС

АВ+АМ+ВС+СМ=23

АВ+АМ+ВМ=18

ВС+СМ+ВМ=17

АВ+АМ=18-ВМ

ВС+СМ=17-ВМ

18-ВМ+17-ВМ=23

35-2ВМ

-2ВМ=23-35

-2ВМ=-12

ВМ=6

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Answer 2

Problem Analysis

We are given a triangle with a perimeter of 23 cm. The triangle is divided by a median into two smaller triangles, with perimeters of 18 cm and 17 cm. We need to find the length of the median.

Solution

To solve this problem, we can use the fact that the medians of a triangle divide each other in a 2:1 ratio. This means that the length of the median is two-thirds of the length of the segment it divides.

Let's assume the length of the median is "m" cm. Then, the length of the segment it divides in the larger triangle is 2m cm, and the length of the segment it divides in the smaller triangle is m cm.

We can set up the following equation based on the given information:

2m + m = 23

Simplifying the equation, we get:

3m = 23

Solving for "m", we find:

m = 23 / 3

Therefore, the length of the median is 23/3 cm.

Verification

Let's verify our solution using the given information. We know that the perimeters of the two smaller triangles are 18 cm and 17 cm. If we add these two perimeters together, we should get the perimeter of the larger triangle.

18 + 17 = 35

The perimeter of the larger triangle is 35 cm. Now, let's calculate the perimeter of the larger triangle using the length of the median we found.

2 * (23/3) + (23/3) = 46/3 + 23/3 = 69/3 = 23

The perimeter of the larger triangle is also 23 cm, which matches the given information. Therefore, our solution is verified.

Conclusion

The length of the median of the given triangle is 23/3 cm.