Question
Download Solution PDFThe area of the trapezium is \(105 \mathrm{~cm}^{2}\) and its height is 7 cm. If one of the parallel sides is longer than the other by 6 cm ，then the sum of the parallel sides is ：
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Area of trapezium = 105 cm2.
Height of trapezium = 7 cm.
Difference between the lengths of the parallel sides = 6 cm.
Formula Used:
Area of trapezium = 0.5 × (Sum of parallel sides) × Height
Calculation:
Let the length of the shorter parallel side be x cm.
Then, the length of the longer parallel side = x + 6 cm.
Sum of parallel sides = x + (x + 6) = 2x + 6.
Area of trapezium = 0.5 × (Sum of parallel sides) × Height
⇒ 105 = 0.5 × (2x + 6) × 7
⇒ 105 = (2x + 6) × 3.5
⇒ 105 / 3.5 = 2x + 6
⇒ 30 = 2x + 6
⇒ 2x = 30 - 6
⇒ 2x = 24
⇒ x = 24 / 2
⇒ x = 12
Sum of parallel sides = 2x + 6
⇒ Sum of parallel sides = 2 × 12 + 6
⇒ Sum of parallel sides = 24 + 6
⇒ Sum of parallel sides = 30
The sum of the parallel sides is 30 cm.
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