CBSE Class 10 Answered

In an equilateral triangle ABC, AD on on BC is constucted such that BD=1/3 BC. Prove That 9AD^2= 7AB^2

Asked by NISHANT Kashyap | 22 Aug, 2014, 09:48: PM

Expert Answer

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.

D r a w space A F space p e r p e n d i c u l a r space t o space B C B y space P y t h a g o r a s space T h e o r e m comma A F squared equals A B squared minus B F squared space space space space space space space equals A B squared minus open parentheses B D plus D F close parentheses squared space space space space space space space space equals A B squared minus B D squared minus D F squared minus 2 B D cross times D F space space space space space space space space space space equals A B squared minus fraction numerator A B squared over denominator 9 end fraction minus D F squared minus fraction numerator 2 A B over denominator 3 end fraction cross times fraction numerator A B over denominator 6 end fraction space space space space space open square brackets sin c e comma space B D equals fraction numerator A B over denominator 3 end fraction comma D F equals fraction numerator A B over denominator 6 end fraction close square brackets space space space space space space space space space space space space equals A B squared minus fraction numerator A B squared over denominator 9 end fraction minus D F squared minus fraction numerator A B squared over denominator 9 end fraction..... left parenthesis 1 right parenthesis A l s o space f r o m space t h e space t r i a n g l e comma space A D F comma A F squared equals A D squared minus D F squared..... left parenthesis 2 right parenthesis F r o m space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma A D squared minus D F squared equals A B squared minus fraction numerator A B squared over denominator 9 end fraction minus D F squared minus fraction numerator A B squared over denominator 9 end fraction rightwards double arrow A D squared equals A B squared minus fraction numerator 2 A B squared over denominator 9 end fraction rightwards double arrow 9 A D squared equals 9 A B squared minus 2 A B squared rightwards double arrow 9 A D squared equals 7 A B squared

Answered by Vimala Ramamurthy | 25 Aug, 2014, 09:33: AM

CBSE Class 10 Answered

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CBSE Class 10 Answered

Application Videos

Word Problem on An Equilateral Triangle

Proof of Pythagoras Theorem

Converse of Pythagoras Theorem

Pythagoras Theorem

Concept Videos

Pythagoras Theorem

Deriving Pythagoras Theorem from the concept of similar ...

Application problems on Pythagoras theorem ...

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