Question

AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). Length of each of its diagonal is

(a) 5 units
(b) 3 units
(c) $\sqrt{34}$ units
(d) 4 units

Answer 1

(c) $\sqrt{34}$ units
$A\left(0,3\right),O\left(0,0\right)\text{and}B\left(5,0\right)$ are the three vertices of a rectangle; let C be the fourth vertex.
Then, the length of the diagonal,
$$\begin{gathered} AB=\sqrt{{\left(5-0\right)}^2+{\left(0-3\right)}^2} \\ =\sqrt{{\left(5\right)}^2+{\left(-3\right)}^2} \\ =\sqrt{25+9} \\ =\sqrt{34}\text{units} \end{gathered}$$
Since, the diagonals of rectangle are equal .
Hence, the length of its diagonals is $\sqrt{34}\text{units}$.