what is the length of an equilateral triangle when the area is 45 meters square?
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To find the length of an equilateral triangle when the area is given, we need to make use of the formula:
Area of an equilateral triangle = (√3/4) * a^2
Where "a" represents the length of one side of the equilateral triangle.
In this case, we are given the area as 45 square meters. We can substitute this into the formula as follows:
45 = (√3/4) * a^2
To solve for "a", we can rearrange the equation:
a^2 = 45 * (4/√3)
Now, let's simplify:
a^2 = 60 * √3
To find the value of "a", we take the square root of both sides:
a = √(60 * √3)
Simplifying further:
a ≈ √(60) * √(√3)
a ≈ 7.746 * (√3)
Therefore, the length of one side of the equilateral triangle is approximately 7.746 * (√3) meters when the area is 45 square meters.