it is given that triangle abc similar triangle pqr with bc/qr=1/3 find the ratio of ar(PRQ)/ar(BCA) - Maths - Triangles

Question

it is given that triangle abc similar triangle pqr with
bc/qr=1/3 find the ratio of ar(PRQ)/ar(BCA)

Santosh Kumar · Accepted Answer

$\frac{BC}{QR} = \frac{1}{3}$

As the given triangle ΔABC and ΔPQR are similar.

$∴ \frac{area (Δ ABC)}{area (Δ PQR)} = \frac{(BC)^{2}}{(QR)^{2}} = (\frac{BC}{QR})^{2} = (\frac{1}{3})^{2} = \frac{1}{9} \Rightarrow \frac{area (Δ PQR)}{area (Δ ABC)} = \frac{9}{1}$

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it is given that triangle abc similar triangle pqr with bc/qr=1/3. find the ratio of ar(PRQ)/ar(BCA).