In ΔABC, ∠135°, CA = $5\sqrt{2}$ cm and AB = 7 cm. E and F are midpoints of sides AC and AB, respectively. The length of EF (in cm) is :
Answer & explanation
Correct answer: option 1
By using the cosine rule :-
cos 135º = \(\frac{ 7² + (5√2)² - BC²}{2 × 7 ×5√2 }\)
\(\frac{ -1}{√2 }\) = \(\frac{ 49 + 50 - BC²}{2 × 7 ×5√2 }\)
- 70 = 99 - BC²
BC² = 169
= ± 13
So, BC = 13 cm
By using mid-point theorem,
EF = \(\frac{ BC}{2 }\)
= \(\frac{ 13}{2 }\)
= 6.5 cm