Question:
The perimeter of an equilateral triangle whose area is \(4\sqrt{3}\,\text{cm}^2\) is equal to
The perimeter of an equilateral triangle whose area is \(4\sqrt{3}\,\text{cm}^2\) is equal to
Show Hint
For an equilateral triangle,
\[
A=\frac{\sqrt3}{4}a^2
\]
and
\[
P=3a.
\]
Updated On: Jun 7, 2026
- \(20\) cm
- \(10\) cm
- \(15\) cm
- \(12\) cm
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The Correct Option is D
Solution and Explanation
Concept:
The area of an equilateral triangle of side \(a\) is
\[
A=\frac{\sqrt{3}}{4}a^2
\]
Step 1: Use the given area.
\[ \frac{\sqrt{3}}{4}a^2=4\sqrt{3} \] \[ a^2=16 \] \[ a=4\ \text{cm} \]
Step 2: Find the perimeter.
\[ P=3a=3(4)=12\ \text{cm} \] center minipage0.35
Perimeter \(=12\) cm minipage center
Step 1: Use the given area.
\[ \frac{\sqrt{3}}{4}a^2=4\sqrt{3} \] \[ a^2=16 \] \[ a=4\ \text{cm} \]
Step 2: Find the perimeter.
\[ P=3a=3(4)=12\ \text{cm} \] center minipage0.35
Perimeter \(=12\) cm minipage center
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