Question

3. In the given figure, P and Q are points on the sides AB and AC respectively of a AABC. PQIBC a divides the AABC into 2 parts, equal in area. The ratio of PA:PB​

Answer 1

$Given \: that \: \\ \\ Area \: of \: the \:  Δ APQ  \\ =  Area \: of \: PQCB$

$That \: means \: \\ \\ Area \:  Δ ABC  \\ =  2 \: Area \: of \:  Δ APQ$

$Since \: PQ ∥ BC$

$Therefore$

$\frac{ Area \: of \: △ABC}{Area \: of \: △APQ}  = \frac{PA {}^{2} }{AB {}^{2} } \\ \\ \frac{PA {}^{2} }{AB {}^{2} } = \frac{ Area \: of \: △ABC}{Area \: of \: △APQ} = \frac{1}{2} \\ \\ \frac{PA}{AB} = \sqrt{ \frac{1}{2} }$

$Therefore, \\ \\  PA:AB = 1:  \sqrt{2}$