What is the area of an equilateral triangle whose perimeter is 48 inches?

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What is the area of an equilateral triangle whose perimeter is 48 inches?

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Answer 1 · 2018-08-05T19:20:32

Answer: $64 \sqrt{3}$ $64sqrt(3)$ ${in}^{2}$ $"in"^2$

Explanation:

Consider the formula for the area of an equilateral triangle:
$\frac{s^{2} \sqrt{3}}{4}$ $(s^2sqrt(3))/4$ , where $s$ $s$ is the side length (this can be easily proved by considering the 30-60-90 triangles within an equilateral triangle; this proof will be left as an exercise for the reader)

Since we are given that the perimeter of the equilateral trangle is $48$ $48$ inches, we know that the side length is $\frac{48}{3} = 16$ $48/3=16$ inches.

Now, we can simply plug this value into the formula:
$\frac{s^{2} \sqrt{3}}{4} = \frac{{(16)}^{2} \sqrt{3}}{4}$ $(s^2sqrt(3))/4=((16)^2sqrt(3))/4$

Canceling, a $4$ $4$ from the numerator and the denominator, we have:
$= (16 \cdot 4) \sqrt{3}$ $=(16*4)sqrt(3)$
$= 64 \sqrt{3}$ $=64sqrt(3)$ ${in}^{2}$ $"in"^(2)$ , which is our final answer.

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What is the area of an equilateral triangle whose perimeter is 48 inches?

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Explanation:

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