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The area of a trapezium is 384cm $2$ . If its parallel sides are in the ratio 3: 5 and the perpendicular distance between them is 12cm, then find the smaller of the parallel side.

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30cm

26cm

24cm

15cm

answer is C.

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Detailed Solution

It is given a trapezium.
Area=384cm

2

Parallel sides ratio=3:5.
Let the parallel sides of trapezium be 3x cm and 5x cm.
And we know that,

Area of trapezium= 12 × (s u m of parallel sides) × d i s t a n c e between parallel sides .

384 = 12 × (3 x + 5 x) × 12 ⇒ 384 = 48 x ⇒ 8 = x

The smaller side is 3x.
So, putting the value of x = 8, results in,

3 × 8 = 24

cm.
Thus, the smaller parallel side is 24 cm.
Therefore, the correct option is 3.

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