SSC CGL 2022 PYQ — Question 12

The correct answer is option 3 i.e. 7

Let the length of MN be 'a'.

By using the cosine rule with respect to 135°

Cos135° = $\frac{a^2 + (5\sqrt2)^2 - (13)^2}{2 \times 5\sqrt2 \times a}$

$\frac{-1}{\sqrt2}$ = $\frac{a^2 + 50 - 169}{2 \times 5\sqrt2 \times a}$

⇒ a²  + 10a - 119 = 0

⇒ a²  + 17a - 7a - 119 = 0

⇒(a + 17)(a - 7)= 0

⇒ a = 7