The area of a field in the shape of a trapezium measures $1440\text{ m}^2$. The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is 5 : 3, the length of the longer parallel side is

### Concept & Formula The area of a trapezium is calculated as half the sum of its parallel sides multiplied by the perpendicular distance (height) between them. $$Area = \frac{1}{2} \times (a + b) \times h$$ ### Step-by-Step Solution * **Define Variables:** Since the ratio of the parallel sides is 5:3, let the longer parallel side be $5x$ and the shorter parallel side be $3x$. * **Identify Given Values:** Area = $1440\text{ m}^2$ Height ($h$) = 24 m * **Set up the Equation:** $1440 = \frac{1}{2} \times (5x + 3x) \times 24$ * **Solve for x:** $1440 = \frac{1}{2} \times (8x) \times 24$ $1440 = 4x \times 24$ $1440 = 96x$ $x = \frac{1440}{96} = 15$ * **Calculate the Longer Side:** Longer side = $5x = 5 \times 15 = 75\text{ m}$. ### Exam Strategy & Shortcut Instead of multiplying out $4 \times 24$, simplify early: divide 1440 by 24 to get 60. Now you have $\frac{1}{2} \times 8x = 60 \implies 4x = 60 \implies x = 15$. The longer side is $5 \times 15 = 75$. ### Common Pitfall Solving for $x$ and incorrectly selecting it as the final answer, or multiplying $x$ by 3 to find the shorter side instead of the requested longer side. ### Final Answer Therefore, the correct answer is **75 m**.