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In the above fig. square ABCD is a trape...


In the above fig. `square` ABCD is a trapezium AB ` |\|`CD and its area is 33 `cm^(2)`. 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.

Text Solution

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The correct Answer is:
`AB=7cm,CD=15cm,AD=5cm,BC=5cm`.
`squareABCD` is a trapezium `AB||CD`
`(squareABCD)=(1)/(2)xx(AB+DC)xxAM" "....` (Formula)
`:.33=(1)/(2)xx(x+2x+1)xxx-4`
(Substituting the given values)
`:.66=(3x+1)xxx-4`
`:.3x^(2)+""-11x-70=0" ":.66=3x^(2)-12x+x-4`
`:.3x^(2)-21x+10x-70=0" ":.66=3x^(2)-11x-4`
`:.3x^(2)-11x-70=0`
`:.3x(x-7)+10(x-7)=0`
`:.(x-7)(3x+10)=0`
`:.x=7or3x=-10`
`:.x=-(10)/(3)`
But the length connot be negative.
`:.x=-(10)/(3)` is unacceptable.
`:.x=7`
`AB=7,CD=(2x+1)=(2xx7+1)=15`
`AD=5,BC=(x-2)=7-2=5.`
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