Question:

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

Solution:

(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 $23 \mathrm{~cm}$.