AOBC is a rectangle whose three vertices are vertices $ \mathrm{A}(0,3), \mathrm{O}(0,0) $ and $ B(5,0) $. The length of its diagonal is
(A) 5
(B) 3
(C) $ \sqrt{34} $
(D) 4

Given: 

AOBC is a rectangle whose three vertices are vertices \( \mathrm{A}(0,3), \mathrm{O}(0,0) \) and \( B(5,0) \).

To do: 

We have to find the length of its diagonal.

Solution:

AOBC is a rectangle.

This implies, AB is one of the diagonals.

The length of the diagonal AB $=$ Distance between the points $A(0, 3)$ and $B(5, 0)$.

Using the distance formula,

$d=\sqrt{( x_2-x_1)^2+( y_2-y_1)^2}$

$\Rightarrow AB=\sqrt{ (5-0)^2+( 0-3)^2}$

$\Rightarrow AB=\sqrt{25+9}$

$\Rightarrow AB=\sqrt{34}$

Therefore, the length of its diagonal is $\sqrt{34}$. 

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Updated on: 10-Oct-2022

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