Question

In  ΔABC, medians AD and BE are drawn. If AD = 4,  ∠DAB = π/6 and  ∠ABE = π/3 , then the area of  ΔABC is (in square units)

(a)   64/3√3

(b)   8/3√3

(c)  16/3√3

(d)  32/3√3

Answer 1

Correct option   (d)  32/3√3

Explanation:

In ΔABC,

cos π/6 = AG/AB

√3/2 = 2/3 AD/AB

√3/2 = 2 x 4 /3AB

AB = 16/3√3

Area of ΔABD = 1/2 AB.AD.sin π/6

= 1/2. 16/3√3 . 4.1/2 = 16/3√3 units²

∴ Area of ΔABC = 2 area of ΔABD

= 32/3√3 units²