In `DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta ABC = (9sqrt3)/(2) cm^(2)`, then BC =

Options

A. `6sqrt3 cm`
B. 9 cm
C. 18 cm
D. 27 cm

Answer

B

Explanation

`(1)/(2) bc sin.(2pi)/(3) = (9sqrt3)/(2)`
`rArr bc = 18`
Now, we have `b - c = 3sqrt3`
`rArr b^(2) + c^(2) - 36 = 27` [using (1)]
`rArr b^(2) + c^(2) = 63`
Using cosine rule,
`a^(2) = 63 - 2 xx 18 xx cos 120^(@) = 81`
`rArr a = 9 cm`