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Question

Let ABCD be parallelogram whose equations for the diagonals AC and BD are x+2y=3 and 2x+y=3, respectively. If length of diagonal AC=4 units and area of parallologram ABCD=8 sq. units then the length of other diagonal BD is

A
103
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B
2
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C
203
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D
None of these
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Solution

The correct option is C 203
The above lines can be written as
y=x2+32
y=2x+3
Hence angle between the lines will be
tanα=|2+121+1|
=34 (taking the positive value)
Let P be the point of intersection of the diagonals.
Therefore area of triangle CPB is given by
Area=pc.(pbsinα2)
=84
2.(pbsinα2)=84
pbsinα=2
pb35=2
PB=103
Hence BD will be twice of PB
=203

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