Question

The area of a trapezium is 475 cm² and its height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other.

Answer 1

In the given figure, ABCD is a trapezium with parallel sides AB and CD.



Let the length of CD be x.
Then, the length of AB be x + 4.

Area of trapezium = $\frac{1}{2}\times \mathrm{sum}\mathrm{of}\mathrm{parallel}\mathrm{sides}\times \mathrm{height}$
$$\begin{gathered} \Rightarrow 475=\frac{1}{2}\times \left(x+x+4\right)\times 19 \\ \Rightarrow 475\times 2=19\left(2x+4\right) \\ \Rightarrow 950=38x+76 \\ \Rightarrow 38x=950-76 \\ \Rightarrow 38x=874 \\ \Rightarrow x=\frac{874}{38} \\ \Rightarrow x=23 \end{gathered}$$

∴ The length of CD is 23 cm and the length of AB is 27 cm.

Hence, the lengths of two parallel sides is 23 cm and 27 cm.