Question

Find the length of parallel sides of a trapezium, if the length of one parallel side is 3 times that of the other. Given that area of the trapezium is $100{\text{m}}^2$ and height is 5 m.

• A. 2 m, 6 m
• B. 3 m, 9 m
• C. 5 m, 15 m
• D. 10 m, 30 m

Answer 1

The correct option is D 10 m, 30 m

Let the length of one parallel side be $y.$ Then, by question, the length of the other parallel side will be $3y.$
$\text{Area of a trapezium}=\frac{1}{2}\times \text{Sum of parallel sides}\times \text{height}$
$⟹100=\frac{1}{2}\times (y+3y)\times 5$
$⟹100=\frac{1}{2}\times 4y\times 5$
$⟹y=\frac{100\times 2}{4\times 5}=10\text{m}$
Hence, the length of the other parallel side is $3y=3\times 10=30\text{m}.$
Thus, the lengths of the parallel sides are 10 m and 30 m.