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CBSE Class 9 Answered

find a percentage increase in the area of a triangle if its each side is doubled ?
Asked by meghnananavati | 08 Jun, 2018, 10:34: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let space the space sides space of space the space triangle space be space straight x comma space straight y space and space straight z. semi minus perimeter space is straight s space equals space fraction numerator straight x space plus space straight y space plus space straight z over denominator 2 end fraction If space the space sides space are space doubled space then space the space new space triagle space has space sides space 2 straight x comma 2 straight y space and space 2 straight z. straight s subscript 1 equals fraction numerator 2 straight x space plus space 2 straight y space plus space 2 straight z over denominator 2 end fraction equals straight x space plus space straight y space plus space straight z space equals space 2 straight s space Area space of space left parenthesis space old space triangle space right parenthesis space equals square root of straight s space left parenthesis space straight s space minus straight a right parenthesis space left parenthesis straight s space minus straight b right parenthesis space left parenthesis straight s space minus straight c right parenthesis end root Area space of space left parenthesis space new space triangle space right parenthesis space equals square root of straight s subscript 1 left parenthesis space straight s subscript 1 space minus straight a right parenthesis space left parenthesis straight s subscript 1 space minus straight b right parenthesis space left parenthesis straight s subscript 1 space minus straight c right parenthesis end root space equals square root of 2 straight s space left parenthesis space 2 straight s space minus straight a right parenthesis space left parenthesis 2 straight s space minus straight b right parenthesis space left parenthesis 2 straight s space minus straight c right parenthesis end root space equals space square root of 16 space straight s left parenthesis straight s space minus space straight a right parenthesis space left parenthesis space straight s minus space straight b right parenthesis space left parenthesis space straight s space minus space straight c right parenthesis end root space equals space 4 space Area space of space left parenthesis space old space triangle space right parenthesis space Therefore space Increase space in space the space area space of space the space triangle space equals Area space of space left parenthesis space new space triangle space right parenthesis space minus space Area space of space left parenthesis space old space triangle space right parenthesis space space equals space 4 space Area space of space left parenthesis space old space triangle space right parenthesis space minus space Area space of space left parenthesis space old space triangle space right parenthesis space space space equals space 3 Area space of space left parenthesis space old space triangle space right parenthesis space space Hence comma space percentage space increase space in space Area space equals left parenthesis space fraction numerator 3 Area space of space left parenthesis space old space triangle space right parenthesis space space over denominator Area space of space left parenthesis space old space triangle space right parenthesis space space end fraction cross times space 100 space right parenthesis space equals space 300 percent sign end style
Answered by Yasmeen Khan | 09 Jun, 2018, 01:12: PM

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