38. Exemplar Exercise Problems XXIV

The dimensions of a rectangle $ABCD$ are $51 cm \times 25 cm$. A trapezium $PQCD$ with its parallel sides $QC$ and $PD$ in the ratio $9 : 8$, is cut off from the rectangle as shown in the figure. If the area of the trapezium $PQCD$ is $56$ th part of the area of the rectangle, find the lengths $QC$ and $PD$.

 

 

$QC=$ $cm$

 

$PD=$ $cm$