Calculate the medians of a triangle with sides 25 cm 25 cm 14 cm.

| January 4, 2021 | education

In an isosceles triangle, the height drawn to the base is also the median of the triangle, then AP = CP = AC / 2 = 14/2 = 7 cm.
In a right-angled triangle ABP, we determine the length of the leg BP.
BP ^ 2 = AB ^ 2 – AP ^ 2 = 625 – 49 = 576.
BP = 24 cm.
Let’s define the area of ​​the triangle ABC. Saws = AC * BP / 2 = 14 * 24/2 = 168 cm2.
The median divides the triangle into two equal sizes, then Sams = Saws / 2 = 168/2 = 84 cm2.
Sams = AC * MN / 2.
MH = 2 * Sams / AC = 2 * 84/14 = 12 cm.
MH is the middle line of the HRV triangle, then PH = CH = PC / 2 = 7/2 = 3.5 cm.Then AH = 7 + 3.5 = 10.5 cm.
In a right-angled triangle AMN, AM ^ 2 = AH ^ 2 + MH ^ 2 = 110.25 + 144 = 254.25 = 254 (25/100) = 25425/100 = 225 * 113/100.
AM = 15 * √113 / 10 = 3 * √113 / 2 cm.
Answer: The medians of the triangle are 24 cm and 3 * √113 / 2 cm.



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