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If the rectangle AOBC has three vertices, i.e., $A (0, 3), O (0, 0)$ and $B (5, 0)$ and, then what is the length of its diagonal?

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34

answer is C.

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Detailed Solution

We have been given,
The rectangle AOBC has three vertices,

A (0, 3), O (0, 0)

and

B (5, 0)

.
Using the distance formula,

D = x 2 − x 1 2 + y 2 − y 1 2

.
The distance between the points and the diagonal length together make up the diagonal length.
The diagonal is thus AB.
Substituting

x_{2} = 5, x_{1} = 0, y_{2} = 0, and y_{1} = 3

, in the formula,

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

\Rightarrow \sqrt{34}

Therefore, the length of its diagonal is

34

.
Hence, option 3 is correct.

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