The median of a triangle with a perimeter of 60 cm splits it into two triangles.
| April 2, 2021 | education
The median of a triangle with a perimeter of 60 cm splits it into two triangles. whose perimeters are 36 cm and 50 cm. What is the length of this median?
1. A, B, C – the vertices of the triangle. ВK median. Perimeters of triangles ABC = 60cm, AВK = 36cm, СВK = 50cm.
2. AB + AK + ВK = 36 cm – the perimeter of the AВK triangle.
3. ВС + СK + ВK = 50 cm – the perimeter of the СВK triangle.
4. Add these expressions:
AB + BC + AK + СK + 2СK = 86 cm.
AK + СK = AC.
5. We replace the AC with AK + СK:
AB + BC + AC + 2BK = 86 cm. AB + BC + AC – the perimeter of the ABC triangle, equal to 60 cm.
60 + 2ВK = 86 cm.
2ВК = 26 cm.
ВK = 13 cm.
Answer: the length of the median VK is 13 cm.
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