# 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

#### Complete Python Prime Pack

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack

9 Courses     2 eBooks

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 $\sqrt{34}$.

Updated on 10-Oct-2022 13:28:26