Tick (✓) the correct answer:
The area of a trapezium is 180 cm2 and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm, the length of the longer of the parallel sides is
(a) 17 cm
(b) 23 cm
(c) 18 cm
(d) 24 cm
(b) $23 \mathrm{~cm}$
Let the length of the parallel sides be $x \mathrm{~cm}$ and $(x+6) \mathrm{cm}$, respectively.
Then, area of the trapezium $=\left\{\frac{1}{2} \times(x+x+6) \times 9\right\} \mathrm{cm}^{2}$
$=\left\{\frac{1}{2} \times(2 x+6) \times 9\right\} \mathrm{cm}^{2}$
$=4.5(2 x+6) \mathrm{cm}^{2}$
$=(9 x+27) \mathrm{cm}^{2}$
But it is given that the area of the trapezium is $180 \mathrm{~cm}^{2}$.
$\therefore 9 x+27=180$
$\Rightarrow 9 x=(180-27)$
$\Rightarrow 9 x=153$
$\Rightarrow x=\frac{153}{9}$
$\Rightarrow x=17$
Therefore, the length of the parallel sides are $17 \mathrm{~cm}$ and $(17+6) \mathrm{cm}$, which is equal to $23 \mathrm{~cm}$.
Hence, the length of the longer parallel side is $23 \mathrm{~cm}$.
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