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prove that perimeter of a triangle is greater than the sum of its three median? ​

Answer 1

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Maths

Quadrilaterals

Mid Point Theorem

Prove that perimeter of a t...

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Prove that perimeter of a triangle is greater than sum of its three medians.

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ANSWER

In the triangle ABC, D,E and F are the midpoints of sides BC,CA and AB respectively.

We know that the sum of two sides of a triangle is greater than twice the median bisecting the third side,

Hence in triangle ABD, AD is a median

⇒AB+AC>2(AD)

Similarly, we get

⇒BC+AC>2(CF)

⇒BC+AB>2(BE)

On adding the above inequations, we get

(AB+AC)+(BC+AC)+(BC+AB)>2AD+2CF+2BE

2(AB+BC+AC)>2(AD+BE+CF)

∴AB+BC+AC>AD+BE+CF

Then perimeter of a triangle is greater than sum of its three medians

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Answer 2

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