Question

The diagonals PR and QS of the rectangle PQRS intersect at O.


(1) If l (PR) = 5, then l(QS) = ?
(2) l (OQ) and l (OR) = ?

Answer 1

(1) Given, l (PR) = 5
Diagonals of a rectangle are congruent.
∴ l (QS) = l (PR) = 5

(2) l (OQ) and l (OR) = ?
Diagonals of a rectangle bisect each other.
∴ l (OQ) = l (OS) = $\frac{1}{2}\times l\left(\mathrm{QS}\right)$
$=\frac{1}{2}\times 5$
= 2.5
And l (OR) = l (OP) = $\frac{1}{2}\times l\left(\mathrm{PR}\right)$
$=\frac{1}{2}\times 5$
= 2.5