JAMB Mathematics 2023 Paper

Concept:The area of a trapezium depends on the average length of its parallel sides multiplied by the perpendicular height.Explanation:Let the parallel sides be $a$ and $b$.Use the trapezium area formula:$$\text{Area} = \frac{1}{2}(a + b)h$$Given: Area $= 200 \, \text{cm}^2$ and height $h = 16 \, \text{cm}$.Substitute the values:$$\frac{1}{2}(a + b) \times 16 = 200$$Simplify:$$8(a + b) = 200$$$$a + b = 25 \quad \text{--- (1)}$$The sides are in the ratio $2 : 3$, so let $a = 2x$ and $b = 3x$.Then from (1):$$2x + 3x = 25$$$$5x = 25$$$$x = 5$$Therefore:$$a = 2 \times 5 = 10 \, \text{cm}$$$$b = 3 \times 5 = 15 \, \text{cm}$$The lengths of the parallel sides are $10 \, \text{cm}$ and $15 \, \text{cm}$.Answer:A. $10 \, \text{cm}$ and $15 \, \text{cm}$