The area of a triangle is `sqrt3` sq. units and `angleB` If `a^(2),b^(2),c^(2)` are in A.P., the length of side AC is

Options

A. `2sqrt3` units
B. 2 units
C. 3 units
D. `3sqrt3` units

Explanation

We have,
`Delta=sqrt3rArr1/2acsinB=sqrt3rArracsin60^(@)=2sqrt3rArrac=4`
Now,
`a^(2),b^(2),c^(2)` are in A.P.
`rArr2b^(2)=a^(2)+c^(2)`
`rArra^(2)+c^(2)-b^(2)=b^(2)`
`rArr(a^(2)+c^(2)-b^(2))/(2ac)=(b^(2))/(2ac)`
`rArrcosB=(b^(2))/(2ac)rArrcos60^(@)=(b^(2))/(2ac)rArrb^(2)=ac`
`rArrb^(2)=4 [becauseac=4]`
`rArrb=2`