10th Class Mathematics Triangles Question Bank Case Based (MCQs) - Triangles

In relation to the part \[(3),\] the ratio of sides \[\text{DF}:\text{AC}\] is:

A) \[2:5\]

B) \[5:2\]

C) \[2:3\]

D) \[3:2\]

Correct Answer: C

Solution :

As triangles ABC and DEF are similar, sides are proportional.

\[\therefore \,\,\,\frac{DE}{AB}=\frac{DF}{AC}\,\,\,\,\Rightarrow \,\,\frac{10}{15}=\frac{DF}{AC}\,\,\Rightarrow \frac{DF}{AC}=\frac{2}{3}\]

Thus, the ratio of sides \[DF:AC=2:3\].

So, option [c] is correct,