Question
In a trapezium, the ratio of the lengths of two parallel
sides is 2:5. The height, measured as the perpendicular distance between these parallel sides, is 24 cm. Given that the area of the trapezium is 1,344 cm², calculate the difference in lengths between the two parallel sides.Solution
Let the parallel sides of trapezium be 2a and 5a cm respectively. Area of trapezium = (1/2) X (sum of parallel sides) X (distance between parallel sides) So, (1/2) X (5a + 2a) X 24 = 1,344 Or, 7a X 12 = 1,344 Or, 7a = 112 So, 'a' = 16 Therefore, required difference = 5a - 2a = '3a' = 3 X 16 = 48 cm
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