The ratio of the length of the parallel sides of a trapezium is 5 : 3 and the perpendicular distance between them is 16 cm. If the area of the trapezium is $960 c m^{2}$ , find the length of the parallel sides.

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Solution

Area of trapezium will be
$= \frac{1}{2} \times s u m o f p a r a l l e l s i d e s \times d i s t a n c e b e t w e e n t h e p a r a l l e l s i d e s$
Let the ratio constant be x.
Thus, the length of the parallel sides will be (5x) cm and (3x) cm.
The perpendicular distance between the parallel sides is 16 cm.
Area of trapezium
$= \frac{1}{2} \times (5 x + 3 x) \times 16 = 960 c m^{2}$
Therefore,
$4 x \times 16 = 960 o r, 4 x = 60 o r, x = 15$
So, Length of the parallel sides are 75 cm and 45 cm.

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