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The area of a trapezium is $121\ cm^2$ and its height is 11 cm. If one of the parallel sides is shorter than the other by 10 cm, find the two parallel sides.
Given:
The area of a trapezium is $121\ cm^2$ and its height is 11 cm.
One of the parallel sides is shorter than the other by 10 cm.
To do:
We have to find the two parallel sides.
Solution:
Let the length of the shorter parallel side be $x$ cm.
This implies,
Length of the longer parallel side $=x+10$ cm.
Area of a trapezium $=\frac{1}{2}\times$ height $\times$ (Sum of the parallel sides)
$121=\frac{1}{2}\times11\times(x+x+10)$
$121\times2=11(2x+10)$
$2x+10=22$
$2x=22-10$
$2x=12$
$x=6$
$\Rightarrow x+10=6+10=16$
The lengths of the two parallel sides are 6 cm and 16 cm.
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