Height from the perimeter — Mensuration Aptitude Question
Height from the perimeter: An equilateral triangle has a perimeter of 36 cm. What is its height? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
An equilateral triangle has a perimeter of 36 cm. What is its height?
Options
- 6√3 cm
- 8√3 cm
- 10√3 cm
- 12√3 cm
Show the answer and the worked solution
Correct answer: A. 6√3 cm
Worked solution
- Side = 36 ÷ 3 = 12 cm.
- Height = (√3/2) × 12 = 6√3 cm (about 10.38 cm).
Answer: 6√3 cm.
The idea
For an equilateral triangle, height is (√3/2)a and area is (√3/4)a². Both follow once the side is known.
Shortcut. The height splits the triangle into two 30-60-90 halves whose short leg is 6 cm; the long leg is √3 times it, 6√3 cm.
Common trap. "12√3 cm" — multiplying the 12 cm side by √3 and forgetting the half in (√3/2) × side.