A) \[9\]
B) \[3\]
C) \[\frac{1}{3}\]
D) \[\frac{1}{9}\]
Correct Answer: A
Solution :
[a] Given, \[\angle ABC-\Delta PQR\]and \[\frac{BC}{QR}=\frac{1}{3}\] |
We know that, the ratio of the areas of two similar triangles is equal to square of the ratio of their corresponding sides. |
\[\therefore \,\,\,\,\,\,\,\,\,\frac{ar(\Delta PQR)}{ar(\Delta ABC)}=\frac{{{(QR)}^{2}}}{{{(BC)}^{2}}}\] |
\[={{\left( \frac{QR}{BC} \right)}^{2}}={{\left( \frac{3}{1} \right)}^{2}}=\frac{9}{1}=9\] |
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