question_answer

 

Directions: Each of these questions contains two statements:

Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

Assertion [A] In \[\Delta ABC\], \[\angle B=90{}^\circ \] and \[BD\bot AC\]. If AD = 4 cm and CD = 5 cm, then BD is \[2\sqrt{5}\] cm.

Reason [R] If a line divides any two sides of a triangle in the same ratio, then the line must not be parallel to the third side.

 

A) A is true, R is true; R is a correct explanation for A.

B) A is true, R is true; R is not a correct explanation for A.

C) A is true; R is False.

D) A is false; R is true.

Correct Answer: C

Solution :

\[\Delta ABC\] is similar to \[\Delta ADB\]

\[\therefore \,\,\,\frac{AB}{AD}=\frac{AC}{AB}\]

\[A{{B}^{2}}=AD\times AC\]

\[A{{B}^{2}}=4\times 9\]

AB = 6 cm

In \[\Delta ADB,\] \[A{{B}^{2}}=A{{D}^{2}}+B{{D}^{2}}\]

\[36\text{ }=\text{ }16\text{ }+\text{ }B{{D}^{2}}\]

\[B{{D}^{2}}\text{ }=\text{ }20\]

\[BD=2\sqrt{5}\,cm\]

Hence, Statement I is true and Statement II is false.