SSC CGL 2021 PYQ — Question 53

The correct answer is option 3 i.e. 15 cm.

From the given figure one can say that,

BD = x, then DC = 2x

AB = AC = BC = 3x.

By using the cosine rule in $\Delta$ABD,

Cos60° = $\frac{x^2 + (3x)^2 - (5\sqrt7)^2}{2 \times x \times 3x}$

1/2 = (x² + 9x² - 175)/6x² 

x² = 25

x = 5

Side of an equilateral triangle = 3x = 3 × 5 = 15 cm.