Question
In ΔABC and ΔPQR, ∠B = ∠Q, ∠C = ∠R. M is the midpoint on QR, If AB : PQ = 7 : 4, then $$\frac{{{\text{area}}\,\left( {\vartriangle ABC} \right)}}{{{\text{area}}\,\left( {\vartriangle PMR} \right)}}$$  is :
Answer: Option D
$$\eqalign{
& \frac{{{\text{area}}{\mkern 1mu} \left( {\vartriangle ABC} \right)}}{{{\text{area}}{\mkern 1mu} \left( {\vartriangle PMR} \right)}} \cr
& = \frac{{{{\left( 7 \right)}^2}}}{{\frac{1}{2} \times {{\left( 4 \right)}^2}}} \cr
& = \frac{{49}}{8} \cr} $$
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$$\eqalign{
& \frac{{{\text{area}}{\mkern 1mu} \left( {\vartriangle ABC} \right)}}{{{\text{area}}{\mkern 1mu} \left( {\vartriangle PMR} \right)}} \cr
& = \frac{{{{\left( 7 \right)}^2}}}{{\frac{1}{2} \times {{\left( 4 \right)}^2}}} \cr
& = \frac{{49}}{8} \cr} $$
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