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

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

Solution:

(c) $\sqrt{34}$ units

$A(0,3), O(0,0)$ and $B(5,0)$ are the three vertices of a rectangle; let $C$ be the fourth vertex.

Then, the length of the diagonal,

$A B=\sqrt{(5-0)^{2}+(0-3)^{2}}$

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

$=\sqrt{25+9}$

$=\sqrt{34}$ units

Since, the diagonals of rectangle are equal .

Hence, the length of its diagonals is $\sqrt{34}$ units.