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CBSE Class 9 Answered

Prove that thrice the median of a triangle is less than twice its perimeter.
Asked by mandaokar | 24 Aug, 2017, 06:41: PM
answered-by-expert Expert Answer
 
begin mathsize 16px style Note colon space Please space check space your space question. The space sum space of space any space two space sides space of space straight a space triangle space is space greater space than space twice space the space median space bisecting space the space third space side. Now comma space AD space is space the space median space bisecting space BC rightwards double arrow AB plus AC greater than 2 AD space space space space space space space space space.... left parenthesis straight i right parenthesis BE space is space the space median space bisecting space AC rightwards double arrow AB plus BC greater than 2 BE space space space space space space space space space.... left parenthesis ii right parenthesis CF space is space the space median space bisecting space AB rightwards double arrow BC plus AC greater than 2 CF space space space space space space space space space.... left parenthesis iii right parenthesis Adding space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis comma space we space get AB plus AC plus AB plus BC plus BC plus AC greater than 2 AD plus 2 BE plus 2 CF rightwards double arrow 2 left parenthesis AB plus BC plus AC right parenthesis greater than 2 left parenthesis AD plus BE plus CF right parenthesis rightwards double arrow AB plus BC plus AC greater than AD plus BE plus CF end style
Answered by Rashmi Khot | 28 Aug, 2017, 09:36: AM

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CBSE 9 - Maths
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CBSE 9 - Maths
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CBSE 9 - Maths
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CBSE 9 - Maths
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CBSE 9 - Maths
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CBSE 9 - Maths
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CBSE 9 - Maths
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