10th Class Mathematics Triangles Question Bank MCQs - Triangles

It is given that \[\Delta ABC\tilde{\ }\Delta PQR\]with \[\frac{BC}{QR}=\frac{1}{3}.\] Then \[\frac{ar\,(\Delta PQR)}{ar(\Delta ABC)}\] is equal to: (NCERT EXEMPLAR)

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.

\[\therefore \,\,\,\,\,\,\,\,\,\frac{ar(\Delta PQR)}{ar(\Delta ABC)}=\frac{{{(QR)}^{2}}}{{{(BC)}^{2}}}\]

\[={{\left( \frac{QR}{BC} \right)}^{2}}={{\left( \frac{3}{1} \right)}^{2}}=\frac{9}{1}=9\]