CTET 2 Math and Science Jul 2019 Paper

Let the longer side of trapezium = a cm and the length of other side = b cm
∵ Area of trapezium $\frac{1}{2}$ × sum of parallel sides × height
Then, $\frac{1}{2}\left(\mathit{a}+\mathit{b}\right)\times \mathit{h}=105$
$\frac{1}{2}\left(\mathit{a}+\mathit{b}\right)\times 7=105$
$\mathit{a}+\mathit{b}=30$...(1)
Given that, a – b = 6 ...(2)
After solving eq. (1) and eq. (2), we get
a = 18, b = 12
∴ The length of longer side = 18 cm.