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Question
In the adjoining fig. `square` ABCD is a trapezium AB || CD and its area is 33 cm2. From the information given in the figure find the lengths of all sides of the `square` ABCD. Fill in the empty boxes to get the solution.
Solution: `square` ABCD is a trapezium.
AB || CD
`"A"(square "ABCD") = 1/2 ("AB" + "CD") xx`______
33 = `1/2 ("x" + 2"x" + 1) xx `______
∴ ______ = (3x + 1) × ______
∴ 3x2 +______ − ______ = 0
∴ 3x(______) + 10(______) = 0
∴ (3x + 10) (______) = 0
∴ (3x + 10) = 0 or ______ = 0
∴ x = `-10/3` or x = ______
But length is never negative.
∴ `"x" ≠ -10/3`
∴ x = ______
AB = ______, CD = ______, AD = BC = ______
Solution
`square` is a trapezium.
AB || CD
`"A"(square "ABCD") = 1/2 ("AB" + "CD") xx bb"AM"`
33 = `1/2 ("x" + 2"x" + 1) xx bb(("x" - 4))`
∴ 66 = (3x + 1) × (x − 4)
∴ 66 = 3x(x − 4) + 1(x − 4)
∴ 0 = 3x2 − 12x + 1x − 4 − 66
∴ 0 = 3x2 − 11x − 70
∴ 3x2 − 11x − 70 = 0
∴ 3x2 − 21x + 10x − 70 = 0 .....`[(-21 xx 10 = -210),(-21 + 10 = -11)]`
∴ 3x(x − 7) + 10(x − 7) = 0
∴ (3x + 10) (x − 7) = 0
∴ (3x + 10) = 0 or (x − 7) = 0
∴ 3x = -10 or x = 7
∴ x = `-10/3` or x = 7
But length is never negative.
∴ `"x" ≠ -10/3`
∴ x = 7
AB = 7, CD = 15, AD = BC = 5
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