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Question
The area of a trapezium is 180 sq.cm and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm. Find the length of the parallel sides.
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Solution
Let one of the parallel side be ‘a’ cm.
Given one parallel sides is longer than the other by 6 cm.
i.e. b = a + 6 cm
Also given height ‘h’ = 9 cm
Area of trapezium = 180 sq.cm
`1/2 xx "h" xx ("a" + "b")` = 180 cm2
`1/2 xx 9 xx ("a" + "a" + 6)` = 180
`1/2 xx 9 xx (2"a" + 6)` = 180
2a + 6 = `(180 xx 2)/9`
= 20 × 2
2a + 6 = 40
2a = 40 – 6
= 34
a = `34/2`
= 17 cm
b = a + 6
= 17 + 6
= 23 cm
∴ The parallel sides are a = 17 cm and b = 23 cm
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