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State true or false.

The perimeter of a triangle is greater than the sum of its three medians.

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True

False

answer is A.

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Detailed Solution

It is given a triangle with medians.
Evaluate by considering

A B C

to be the triangle where

D, E

and

F

are the mid-points of

B C, C A

and

A B

respectively.
Question Image

As it is known that the sum of two sides of the triangle is greater than twice the median bisecting the

3 r d

side.

A B + A C > 2 A D

A C + B C > 2 C F

A B + B C > 2 B E

Evaluate by adding all these.

(A B + B C) + (B C + A C) + (A B + B C) > 2 A D + 2 C F + 2 B E

2 (A B + B C + A C) > 2 A D + 2 C F + 2 B E

A B + B C + C A > A D + C F + B E

Hence, the perimeter of the

Δ A B C

is greater than the sum of its medians.
Hence the statement is true.
Hence option 1 is correct.

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