The area of an equilateral triangle is 16√3 sq cm. What is its perimeter?
24 cm
Equilateral Triangle Perimeter from Area Calculation
The area of an equilateral triangle is given as $16\sqrt{3}$ sq cm.
We need to find its perimeter.
Finding the Side Length
The formula for the area of an equilateral triangle with side length s is:
$ \text{Area} = \frac{\sqrt{3}}{4} s^2 $
Substitute the given area into the formula:
$ 16\sqrt{3} = \frac{\sqrt{3}}{4} s^2 $
To find s, we can rearrange the equation:
- Divide both sides by $\sqrt{3}$: $16 = \frac{1}{4} s^2$
- Multiply both sides by 4: $64 = s^2$
- Take the square root of both sides: $s = \sqrt{64}$
- Calculate the side length: $s = 8$ cm
Calculating the Perimeter
The perimeter of an equilateral triangle is calculated as 3 times the side length.
$ \text{Perimeter} = 3 \times s $
Substitute the calculated side length (s = 8 cm):
$ \text{Perimeter} = 3 \times 8 $
$ \text{Perimeter} = 24 \text{ cm} $
Therefore, the perimeter of the equilateral triangle is 24 cm.
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