prove that three times the sum of the sides of a triangle is equal to four times the sum of squares of the medians of that triangle
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Step-by-step explanation:
In triangle sum of squares of any two sides is equal to twice the square of half of the third side, together with twice the square of median bisecting it.
If AD is the median.
AB² + AC² = 2{AD² + BC²/4}
==> 2(AB² + AC²) = 4AD²+ BC² ---- (1)
If BE and CF are medians,
2(AB² + BC²) = 4BE² + AC² ---- (2)
2(AC² + BC²) = 4CF² + AB² ---- (3)
On adding (1),(2),(3)
3(AB² + BC² + AC²) = 4(AD² + BE² + CF²)
Hence proved.
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question solved and side one is
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