Question : The ratio of the length of the parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. If the area of the trapezium is 450 cm$^2$ the sum of the length of the parallel sides is:
Option 1: 15 cm
Option 2: 36 cm
Option 3: 42 cm
Option 4: 60 cm
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Correct Answer: 60 cm
Solution : Given: Height = 15 cm Area of trapezium = 450 cm$^2$ Let the parallel sides be $3x$ and $2x$. We know that, Area of trapezium = $\frac{1}{2}$ × (Sum of parallel sides) × height $450 = \frac{1}{2}×(3x+2x)×15$ ⇒ $900 = 5x\ ×\ 15$ ⇒ $x=12$ $\therefore$ The parallel sides are 3 × 12 = 36 and 2 × 12 = 24. Sum of parallel sides = 36 + 24 = 60 Hence, the correct answer is 60 cm.
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