Question

The adjacent sides of a parallelogram are $15cm$ and $10cm$. If the distance between the longer sides is $6cm$, find the distance between the shorter sides.

Answer 1

It is given that
$AB=DC=15cm$,
$BC=AD=10cm$,
Here the distance between longer sides $AB$ and $DC$ = $6cm$.
So perpendicular $DL$ = $6cm$.
$DM$ is perpendicular to $BC$,
We know that,
Area of parallelogram = $base\ast altitude$
So we get,
$=AB\ast DL$
Substituting the values,
$=15\ast 6$
$=90c{m}^2$
Consider $DM$ = $x$ $cm$,
Similarly,
Area of parallelogram $ABCD$ = $BC\ast DM$
Substituting the values,
$=10\ast x$
$=10x$ $c{m}^2$
By equating both,
$10x=90$
$x=90/10=9cm$.