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 = ______

Answer 1

`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