Question

AOBC is rectangle whose three vertices are A(0,3), O(0,0) and B(5,0). The length of each of its diagonals is

(a) 5 units 

(b) 3 units 

(c) 4 units 

(d) √34 units

Answer 1

Correct answer is (C) 4 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,

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

= \(\sqrt{(5)^2+(-3)^2}\)

= \(\sqrt{25+9}\)

= \(\sqrt{34}\) units

Since, the diagonals al rectangle is equal.

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