Question

The area of a trapezium is 384 cm². Its parallel sides are in the ratio 3 : 5 and the perpendicular distance between them is 12 cm. Find the length of each one of the parallel sides.

Answer 1

$$\begin{gathered} \text{Given:} \\ {\text{Area of the trapezium = 384 cm}}^2 \\ \text{The parallel sides are in the ratio 3:5 and the perpendicular height between them is 12 cm.} \\ \text{Suppose that the sides are in x multiples of each other.} \\ \text{Then, length of the shorter side = 3x} \\ \text{Length of the longer side = 5x} \\ \text{Area of a trapezium=}\frac{1}{2}\text{×(Sum of parallel sides)×(Height)} \\ \Rightarrow 384=\frac{1}{2}\times \text{(3x+5x)×(12)} \\ \Rightarrow \text{384=}\frac{12}{2}\text{×(8x)} \\ \Rightarrow \text{384=}\mathrm{6\times (8x)} \\ \Rightarrow \text{8}x=\frac{384}{6}\text{=64} \\ \Rightarrow x\text{=}\frac{64}{8}\text{=8 cm} \\ \therefore \text{Length of the shorter side=3×x=3×8=24 cm} \\ \text{And, length of the longer side=5×x=5×8=40 cm} \end{gathered}$$