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 : |
6.5 5.5 6 5 |
6.5 |
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 |