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

If \[\text{AL}=\text{b},\]then find b in terms of x, y and d is:

A) \[\frac{zd}{y}\]

B) \[\frac{yd}{z}\]

C) \[xyd\]

D) \[xzd\]

Correct Answer: A

Solution :

By AA-similarity criterion,

\[\Delta ALO\tilde{\ }\Delta ACD\]

\[\therefore \,\,\,\frac{AL}{AC}=\frac{OL}{DC}\Rightarrow \frac{b}{z}=\frac{d}{y}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,b=\frac{zd}{y}\]

So, option [a] is correct.