Geometry and TrigonometryHardPerimeter from a tangent and the hypotenuse
Geometry and Trigonometry practice question
In right triangle ABC, the right angle is at C, tan A = 3/4, and AB = 25. What is the perimeter of the triangle?
Answer: 60
tan A = 3/4 means the legs are in the ratio 3 to 4, a 3-4-5 triangle scaled by 5: legs 15 and 20. The perimeter is 15 + 20 + 25 = 60.
Common wrong answers
- If you answered 32
- 32 uses legs 3 and 4 with the hypotenuse 25.
- If you answered 35
- 35 adds the legs only.
- If you answered 50
- 50 doubles the hypotenuse.
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