10th Class Mathematics Triangles Question Bank MCQs - Triangles

If triangle \[\text{ABC}\] is similar to triangle \[\text{DEF}\] such that \[3AB=DE\]and \[\text{BC}=\text{9 cm},\]then \[\text{EF}\] is equal to:

A) \[\text{27}\,\text{cm}\]

B) \[\text{3 cm}\]

C) \[\text{6 cm}\]

D) \[\text{9 cm}\]

Correct Answer: A

Solution :

[a] \[\Delta ABC\tilde{\ }\Delta DEF\]

\[\therefore \,\,\,\,\,\,\,\,\frac{AB}{DE}=\frac{BC}{EF}\,\,\,\,\,\,\Rightarrow \,\,\frac{AB}{3\,AB}=\frac{9}{EF}\] \[[3AB=DE]\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,EF=27cm\]