The length of the parallel sides of a trapezium are 5cm and 7cm. If its area is 120cm\(^2\), find the perpendicular distance between the parallel sides

The area of a trapezium is given by the formula: $$\text{Area} = \frac{1}{2}(a+b)h$$ where $a$ and $b$ are the parallel sides of the trapezium and $h$ is the perpendicular distance between them. In this question, we are given that $a = 5\text{ cm}$, $b = 7\text{ cm}$, and $\text{Area} = 120\text{ cm}^2$. We need to find $h$. Using the formula above, we can rearrange it to get $h$ as the subject: $$h = \frac{2\text{Area}}{a+b}$$ Substituting the given values, we get: $$h = \frac{2(120)}{5+7} = \frac{240}{12} = 20$$ Therefore, the perpendicular distance between the parallel sides is $20\text{ cm}$. The answer is not among the options given, so it is likely there was an error in one of the values or options presented.