question_answer

If the corresponding medians of two similar triangles are in the ratio \[\text{5}:\text{7},\] then the ratio of their corresponding sides is:                                                              (CBSE 2015)

A) \[\text{25}:\text{49}\]

B) \[\text{5}:7\]

C) \[7:5\]

D) \[\text{49}:\text{25}\]

Correct Answer: B

Solution :

  

[b] Let ABC and PQR are two similar triangles with medians AD and P5 respectively.

Then,         \[\frac{AD}{PS}=\frac{5}{7}\]               (Given)

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{AB}{PQ}=\frac{5}{7}\,\,\,\,\,\,\,\,\,\,\,\,(\Delta ABC\tilde{\ }\Delta PQR)\]

Hence, the ratio of corresponding sides is \[5:7\].