Question:
Tick (✓) the correct answer:
The lengths of the parallel sides of a trapezium are 19 cm and 13 cm and its area is 128 cm2. The distance between the parallel sides is
(a) 9 cm
(b) 7 cm
(c) 8 cm
(d) 12.5 cm
Solution:
(c) 8 cm
Let the distance between the parallel sides be $\mathrm{x} \mathrm{cm}$.
Then, area of the trapezium $=\left\{\frac{1}{2} \times(19+13) \times \mathrm{x}\right\} \mathrm{cm}^{2}$
$=\left(\frac{1}{2} \times 32 \times x\right) \mathrm{cm}^{2}$
$=16 x \mathrm{~cm}^{2}$
But it is given that the area of the trapezium is $128 \mathrm{~cm}^{2} .$
$\therefore 16 x=128$
$\Rightarrow x=\frac{128}{16}$
$\Rightarrow x=8 \mathrm{~cm}$