question_answer

ABCD is a rectangle whose three vertices are \[(4,3),\]\[(4,1)\]and \[(0,1)\]. The length of its diagonal is:  (CBSE 2014)

A) \[2\sqrt{5}\]units

B) \[\sqrt{5}\]units

C) \[\frac{1}{\sqrt{5}}\]units

D) \[\frac{2}{\sqrt{5}}\]units

Correct Answer: A

Solution :

[a] Let the three vertices of rectangle ABCD be \[A(4,3),\]\[B(4,1)\]and \[C(0,1)\].

In right \[\Delta ABC,\]

Length of diagonal \[AC=\sqrt{{{(0-4)}^{2}}+{{(1-3)}^{2}}}\]

(By Pythagoras theorem)

\[=\sqrt{16+4}=\sqrt{20}=2\sqrt{5}\] units