CAT Exam 2021 Slot 3 Solved Paper

Applying cosine rule in triangle ACD,
$100 + x^2 - 2 × 10 × x \cos 30 = 400 $
$x^2 - 10x √3 - 300 = 0 $
Solving, we get $ x = {10√3 + 10√ 15}/2 $
Hence, area = $10 x \sin 30 = ({10√3 + 10\√15}/2) 10 $
$ =25(√3 + √15) $