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
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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