In △ ABC, ∠A = 135º, CA = 5 √(2) cm and AB = 7 cm, E…

In △ ABC, ∠A = 135º, CA = 5 $\sqrt{2}$ cm and AB = 7 cm, E and F are the midpoints of sides AC and AB, respectively. The length of EF (in cm) is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 6.5.

By cosine rule

Cos A = b² + c² - a²/ 2bc

Applying mid-point theorem

EF = 1/2 × BC

Cos 135° = (5√2)² + 7² - a²/ 2 × 7 × 5√2

⇒ $\frac{-1}{\sqrt2}= \frac{(5\sqrt2)^2 + (7)^2 - (a)^2}{2\times7\times5\sqrt2}$

⇒ -70 = 50 + 49 - a²

⇒ a² = 169

⇒ a = 13, a ≠ - 13

EF = 1/2 × 13 cm

EF = 6.5 cm

SSC CHSL 2021 PYQ — Question 68