Question

If $AOBC$ is a rectangle whose three vertices are $A(0,3),O(0,0)$ and $B(5,0)$, then the length of its diagonal is

• A. $5$
• B. $3$
• C. $\sqrt{34}$
• D. $4$

Answer 1

Answer: (C)

$\sqrt{34}$

Given that the three vertices of a rectangle $AOBC$ are

$A(x_1,y_1)=(0,3),B(x_2,y_2)=(5,0)\&O(x_3,y_3)=(0,0)$.

Now the abscissae of $O$ and $A$ are zeros.

So, $OA$ falls along the $Y$ axis.

Similarly, the ordinates of $O$ and $B$ are zeros.

So, $OB$ falls along $X-$axis.

$\therefore \angle AOB={90}^0$

$\therefore AB$ is a diagonal of $AOBC$.

Using distance formula, we have

AB=$\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}=\sqrt{{(5-0)}^2+{(0-3)}^2}$ units $=\sqrt{34}$ units.