If area of ` ΔA B C(Δ)` and angle C are given and if the side `c` opposite to given angle is minimum, then `a=sqrt((2Δ)/(sinC))` (b) `b=sqrt((2Δ)/(sinC))` `a=sqrt((4Δ)/(sinC))` (d) `b=sqrt((4Δ)/(sinC))`

Options

A. `a = sqrt((2Delta)/(sinC))`
B. `b = sqrt((2Delta)/(sinC))`
C. `a = (4Delta)/(sinC)`
D. `b = (4Delta)/(sin^(2)C)`

Answer

A, B

Explanation

`c^(2) = a^(2) + b^(2) - 2ab cos C`
`=(a - b)^(2) + 2ab (1-cos C)`
`=(a -b)^(2) + (4Delta)/(sinC) (1-cosC)`
For c to be minium, `a = b`
Also, `Delta = (1)/(2) ab sin C`
`rArr a^(2) = (2Delta)/(sin C) = b^(2)`