Question

LMNO is a trapezium with $LM\parallel NO$. If P and Q are the mid - points of LO and MN respectively and LM =5 cm and ON =10 cm then PQ =

• A. 2.5 cm
• B. 5 cm
• C. 7.5 cm
• D. 15 cm

Answer 1

The correct option is C

7.5 cm

Join PQ and LN where LN intersects PQ at A. In $\Delta LMN$, A and Q are mid points of LN and MQ.
$\therefore$ By mid point theorem $AQ\parallel LM$ and
$AQ=\frac{1}{2}\left(LM\right)=\frac{1}{2}\left(5\right)=2.5cm$
In $\Delta LON$, P and A are mid points of LO and LN
$\therefore$ By mid point theorem
$AP=\frac{1}{2}\left(ON\right)=\frac{1}{2}\left(10\right)=5cm$
$\therefore$ $PQ=(2.5+5)cm=7.5cm$.