Question 53

The parallel sides of a trapezium are in a ratio 2 : 3 and their shortest distance is 12 cm. If the area of the trapezium is 480 sq. cm, the longer of the parellel sides is of length.

Solution

Let the shorter of the parallel side, $$a = 2x$$ cm

=> Longer of the parallel side, $$b = 3x$$ cm

Height of trapezium, $$h = 12$$ cm

=> Area of trapezium = $$\frac{1}{2} \times h \times (a + b) = 480$$

=> $$\frac{1}{2} \times 12 \times (2x + 3x) = 480$$

=> $$6 \times 5x = 480$$

=> $$x = \frac{480}{30} = 16$$

$$\therefore$$ Longer of the parallel side = $$3 \times 16 = 48$$ cm

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