An equilateral triangle has area 9√3 square centimetres. Find the exact height (altitude) of the triangle.
Aptitude
Area
Difficulty: Easy
Choose an option
-
A6 cm
-
B6√3 cm
-
C3√3 cm
-
D9 cm
Answer
Correct Answer: 3√3 cm
Explanation
Introduction / Context:Converting between area and altitude in an equilateral triangle relies on two linked formulas: A = (√3/4)a^2 and h = (√3/2)a. Use one to find side length, then compute the altitude.
Given Data / Assumptions:
- Area A = 9√3 cm^2.
Concept / Approach:First find the side a from A = (√3/4)a^2. Then use h = (√3/2)a to get the altitude.
Step-by-Step Solution:
9√3 = (√3/4) * a^2 ⇒ a^2 = 36 ⇒ a = 6 cmh = (√3/2) * a = (√3/2) * 6 = 3√3 cmVerification / Alternative check:Compute A from a=6: (√3/4)*36 = 9√3 cm^2; consistent.
Why Other Options Are Wrong:
- 6 cm, 9 cm: These are side-length-like numbers, not the altitude for A = 9√3.
- 6√3 cm: Overshoots by a factor of 2.
Common Pitfalls:Mixing up the area and altitude formulas or skipping the square on a.
Final Answer:3√3 cm