Let ABCD be a parallelogram the equation of whose diagonals are `AC : x+2y =3`; BD: 2x + y = 3. If length of diagonal` AC =4` units and area of `ABCD = 8` sq. units. (i) The length of the other diagonal is (ii) the length of side AB is equal to

Options

A. `10//3`
B. 2
C. `20//3`
D. none of these

Answer

C

Explanation

Angle between the diagonal is given by
`"tan " theta = |(-(1)/(2)+2)/(1+1)| = (3)/(4)`
`"or sin"theta =(3)/(5)`
Area of `DeltaCPB` is
`(1)/(2) xx PC xx PB "sin" theta = 2`
or `PB = (10)/(3)`
or `BD = (20)/(3)`