Question

The area of a trapezium is 91 cm² and its height is 7 cm. If one of the parallel sides is longer than the other by 8 cm, find the two parallel sides.

Answer 1

$$\begin{gathered} \text{Given:} \\ {\text{Area of the trapezium = 91 cm}}^2 \\ \text{Height = 7 cm} \\ \mathrm{Let}\text{the length of the smaller side be}x. \\ \text{Then, the length of longer side will be 8 more than smaller side, i.e. 8+}x. \\ \text{Area of trapezium=}\frac{1}{2}\text{×(Sum of the parallel sides)×(Height)} \\ \Rightarrow \text{91=}\frac{1}{2}\text{×[(8+x)+x]×(7)} \\ \Rightarrow \text{91=}\frac{7}{2}\text{×[8+x+x]} \\ \Rightarrow \text{91×2=7×[8+2x]} \\ \text{We can rewrite it as follows:} \\ \mathrm{7\times [8+2x]}=182 \\ \Rightarrow [8+2x]=\frac{182}{7}=26 \\ \Rightarrow \mathrm{8+2}x=26 \\ \Rightarrow \text{2}x\text{=26-8=18} \\ \Rightarrow x=\frac{18}{2}\text{=9 cm} \\ \therefore \mathrm{L}\text{ength of the shorter side of the trapezium = 9 cm} \\ \text{And, length of the longer side = 8+x = 8+9 = 17 cm} \end{gathered}$$