Question:
The area of a field in the shape of a trapezium measures 1440 m2.The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is \(5:3\), the length of the longer parallel side is
The area of a field in the shape of a trapezium measures 1440 m2.The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is \(5:3\), the length of the longer parallel side is
Updated On: Jan 30, 2025
- 45 m
- 60 m
- 75 m
- 12 m
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The Correct Option is C
Solution and Explanation
The correct option is (C); Let lengths of longer parallel side and shorter side be \(5x\) and \(3x\) m respectively.
Area of trapezium = \(\frac{1}{2}\)\(\times\)(height)\(\times\)(sum of parallel sides)
\(\frac{1}{2}\)\(\times\)24\(\times\)(\(5x\) + \(3x\)) = 1440
12\(\times\)\(8x\) = 1440
\(x\) = 15
\(\therefore\) Length of longer side 15\(\times\)5 = 75 m
Area of trapezium = \(\frac{1}{2}\)\(\times\)(height)\(\times\)(sum of parallel sides)
\(\frac{1}{2}\)\(\times\)24\(\times\)(\(5x\) + \(3x\)) = 1440
12\(\times\)\(8x\) = 1440
\(x\) = 15
\(\therefore\) Length of longer side 15\(\times\)5 = 75 m
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