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 a rhombus of side 15 cm, one of the diagonals is 20 cm long.

The length of the second diagonal is \[\frac{AB}{AD}=\frac{AC}{AE}\]cm.

Reason [R] The sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

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: D

Solution :

According to the question,

Given, AB = BC =CD=DA=15cm

AC = 20 cm [let]

Let BO = OD = x cm

\[\therefore\] In \[\Delta BOC\], \[{{x}^{2}}+{{10}^{2}}={{15}^{2}}\]

[by Pythagoras theorem]

\[{{x}^{2}}=125\]

\[x=5\sqrt{5}\]

\[BD=2x=10\sqrt{5}\,cm\]

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