Question

A(tri.APQ) / A(tri.ABC)=
AP.AQ / AB.AC ​

Answer 1

Given A line cuts two sides AB and AC of triangle ABC at points P and Q respectively. we have to prove that

\frac{Area(APQ)}{Area(ABC)}=\frac{AP\times AQ}{AB\times AC}

By area formula i.e

ar(APQ)=\frac{1}{2}AP\times AQsinA

ar(ABC)=\frac{1}{2}AB\times ACsinA

∴ \frac{Area(APQ)}{Area(ABC)}=\frac{\frac{1}{2}AP\times AQsinA}{\frac{1}{2}AB\times ACsinA}

=\frac{AP\times AQ}{AB\times AC}

Answer 2

Answer:

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