Question

The diagonals of trapezium PQRS where PQ||RS intersect at point O.
The length of OP and OQ is 5 and 4 units respectively. Find the length of OS if the length of OR is 2 units.

• A. 2.4
• B. 3
• C. 1.6
• D. 4

Answer 1

The correct option is C 1.6

Given, PQ||RS, OP = 5, OQ = 4 and OR = 2


Let us take $△ORQ$ and $△OPS$.

$\angle QOR=\angle SOP$ (opposite angles)
$\angle RQO=\angle PSO$ (QR || PS)
$\angle QRO=\angle SPO$ (QR || PS)

Hence, by AAA similarity,
$△ORQ\sim △OPS$

$⟹\frac{OR}{OP}=\frac{OS}{OQ}$

Given,
$OP=5$
$OQ=4$
$OR=2$

$⟹\frac{2}{5}=\frac{OS}{4}$

$⟹OS=1.6$