Geometry and TrigonometryVery hardEqual sides of an isosceles triangle from its height
Geometry and Trigonometry practice question
In triangle ABC, AB = AC. Point D lies on BC so that AD is perpendicular to BC. If BC = 10 and AD = 12, what is the length of AB?
Answer: 13
In an isosceles triangle the altitude bisects the base, so BD = 5, and AB = √(5² + 12²) = 13.
Common wrong answers
- If you answered 12
- 12 is the altitude.
- If you answered 17
- 17 adds 5 and 12.
- If you answered 15.6
- 15.6 uses the whole base: √(10² + 12²).
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