10th Class Mathematics Triangles Question Bank MCQs - Triangles

D and E are respectively the points on the sides AB and AC of a triangle ABC such that \[\text{AD}=2\text{ cm},\] \[\text{BD}=\text{3 cm},\] \[\text{BC}=\text{7}.\text{5 cm}\]and \[DE\left\| BC \right.\].Then length of DE (in cm) is:

A) \[2.5\]

B) \[3\]

C) \[5\]

D) \[6\]

Correct Answer: B

Solution :

[b] \[\frac{AD}{AB}=\frac{DE}{BC}\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\frac{2}{2+3}=\frac{DE}{7.5}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,DE=\frac{2\times 7.5}{5}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,DE=3cm\]