question_answer

ABC is a right angled triangle such that \[AB=a-b,\]\[BC=a\] and \[CA=a+b.\]D is a point on BC such that BD = AB. The ratio of BD : DC for any value of a and b is given by

A) 3 : 2

B) 4 : 3

C) 5 : 4

D) 3 : 1

Correct Answer: D

Solution :

[d] In right angled \[\Delta ABC,\] \[{{(a+b)}^{2}}={{(a-b)}^{2}}+{{a}^{2}}\] \[\Rightarrow \]   \[4b=a\] Now,     \[\frac{BD}{DC}=\frac{a-b}{b}=\frac{4b-b}{b}\] \[=\frac{3b}{b}=\frac{3}{1}=3:1\]