The median of a triangle with a perimeter of 40cm divides it into 2 triangles with a perimeter
| September 14, 2021 | education
The median of a triangle with a perimeter of 40cm divides it into 2 triangles with a perimeter of 30cm and 34cm. Find the length of this median.
1. R -perimeter.
2. P Δ ABC = AC + BC + AB = 40 centimeters.
3. P Δ ABK = AK + BK + AB = 34 centimeters.
4. P Δ СBK = СK + BK + BC = 30 centimeters.
5. P Δ ABK + P Δ СBK = AK + BK + AB + СK + BK + BC = 64 centimeters. AK + СK = AC.
We substitute the AC instead of (AK + СК):
AC + BC + AB + 2BK = 64 centimeters
40 + 2BK = 64 centimeters.
BK = 24: 2 = 12 centimeters.
Answer: the length of the median VC is 12 centimeters.
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