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  • The perimeter of a triangle is greater than the sum of its three medians. (True/False)Option: 1 TrueOpt

The perimeter of a triangle is greater than the sum of its three medians. (True/False)

Option: 1

True


Option: 2

False


Answers (1)

best_answer

Let AD, BE and CF be the three medians of a triangle ABC.

We know that the sum of any two sides of a triangle is greater than twice the median drawn to the third side.

\\\therefore \quad A B+A C>2 A D\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ldots(i)\\\mathrm{}\;\;\;\;\;\;\;A B+B C>2 B E\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ldots(ii)\\ and \;B C+A C>2 C F\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ldots(iii) .

Adding, the corresponding sides of (i), (ii) and (iii), we get

\\\therefore \quad 2(A B+B C+A C)>2(A D+B E+C F)\\ \therefore \quad(A B+B C+A C)>(A D+B E+C F)

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

Posted by

SANGALDEEP SINGH

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