Question

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

Answer 1

$ABCD$ is trapezium, $AB\parallel DC$.

$M$ and $N$ are mid-points of side $AD$ and side $BC$.

Since, the segment joining the mid-points of non-parallel sides of trapezium is half the sum of the length of its parallel sides.

$\Rightarrow$ $MN=\frac{1}{2}(AB+CD)$

$\Rightarrow$ $14=\frac{1}{2}(12+CD)$

$\Rightarrow$ $28=12+CD$

$\therefore$ $CD=16cm$