Question

$\square$ABCD is a trapezium in which AB || DC. M and N are mid-points of side AD and side BC respectively. If AB = 12 cm. and MN = 14 cm, find CD.

Answer 1

We have a trapezium in which AB || CD.
M and N are the midpoints of sides AD and BC, respectively.
Also,
AB = 12 cm and MN = 14 cm

We know that the length of the segment joining the midpoints of the non-parallel sides of a trapezium is half the sum of the lengths of its parallel sides.
Thus, we have:
$\mathrm{MN}=\frac{1}{2}(\mathrm{AB}+\mathrm{CD})$

We know:
MN = 14 and AB = 12
Thus, we have:
$$\begin{gathered} 14=\frac{1}{2}(12+\mathrm{CD}) \\ \Rightarrow 28=12+\mathrm{CD} \\ \Rightarrow \mathrm{CD}=28-12 \\ \Rightarrow \mathrm{CD}=16\mathrm{cm} \end{gathered}$$