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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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