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Question
The area of a trapezium is 91 cm2 and its height is 7 cm. If one of the parallel sides is longer than the other by 8 cm, find the two parallel sides.
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Solution
Given that,
Let the length of one parallel side of the trapezium = x meter
Length of other parallel side of trapezium = (x + 8) meter
Area of trapezium = 91 cm2
Height = 7 cm
We know that,
Area of trapezium = `1/2("Sum of lengths of parallel sides") xx "altitude"`
`91 = 1/2(x + x + 8) xx 7`
91 = `1/2(2x + 8) xx 7`
91 = (x + 4) × 7
(x + 4) = `91/7`
x + 4 = 13
x = 13 - 4
x = 9
∴ Length of one parallel side of trapezium = 9 cm
And, Length of other parallel side of trapezium = x + 8 = 9 + 8 = 17 cm
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