The area of an equilateral triangle is √3. What is the perimeter of the triangle?
(A) 2 (B) 4 (C) 6 (D) 8
Options:
(A) 2
(B) 4
(C) 6
(D) 8
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2018 Q.04)**
**1. Governing Concept & Question Classification**:
- **Section**: General Aptitude (GA)
- **Question Type**: **MCQ** (1 Mark)
- **Topic**: Mensuration & Geometry (Equilateral Triangle Properties)
**2. Detailed Step-by-Step Derivation**:
- Let $s$ be the side length of the equilateral triangle.
- The standard area formula for an equilateral triangle is:
$ ext{Area} = rac{\sqrt{3}}{4} s^2$
- Given that $ ext{Area} = \sqrt{3}$:
$ rac{\sqrt{3}}{4} s^2 = \sqrt{3} \implies s^2 = 4 \implies s = 2 ext{ units}$
- The perimeter of an equilateral triangle is the sum of its three equal sides:
$ ext{Perimeter} = 3 imes s = 3 imes 2 = 6$
- **Option-by-Option Evaluation**:
- **Option (A) [INCORRECT]**: 2 is the length of a single side ($s$), not the perimeter.
- **Option (B) [INCORRECT]**: 4 corresponds to $s^2$, not the perimeter.
- **Option (C) [CORRECT]**: 6 is the exact perimeter ($3 imes 2 = 6$).
- **Option (D) [INCORRECT]**: 8 is an erroneous arithmetic value.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **C**
- **Scoring Criteria**: +1.0 Mark (Negative marking: -0.33 marks).
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