NECO 2004 Mathematics · Question 23
Two angles of a triangle are 45º each and its longest side is 12cm. Find the length of one of the other sides
Options
- A.12cm
- B.9cm
- C.6cm
- D.6cm
- E.3cm
Answer: C. 6cm
Explanation written with AI and checked against the answer key
Analyze the question: Two angles are 45° each, so the third angle is 180° − 45° − 45° = 90°. This is a right-angled isosceles triangle. The longest side is the hypotenuse, which is 12 cm. We need one of the two equal sides. Concept: In a right-angled isosceles triangle with equal sides x, Pythagoras' theorem gives the hypotenuse as x√2. You can also use the sine rule. Solution: Let each equal side be x. x² + x² = 12² 2x² = 144 x² = 72 x = √72 = √(36 × 2) = 6√2 cm Check with the sine rule: x / sin 45° = 12 / sin 90° x = 12 × (√2/2) = 6√2 cm ✓ Answer: The length of one of the other sides is 6√2 cm, which is option C. Tip: For a 45°-45°-90° triangle, the equal sides = hypotenuse ÷ √2 (or hypotenuse × √2/2). So 12 ÷ √2 = 6√2. Remember that the hypotenuse is always the longest side, so the answer must be less than 12. This rules out option A, and 6√2 ≈ 8.49 fits well.AI can make mistakes. Report anything that looks wrong.
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