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Answer :
To find the perimeter of an equilateral triangle with a height of 13 meters, you use the relationship between the side length and height, solve for the side length, and then multiply it by three.
The area of an equilateral triangle can be expressed using the formula A = (sqrt(3)/4) times a², where A is the area, and 'a' is the length of a side. Given the height (h) of 13 meters, we can use the relationship between the side length and height in an equilateral triangle, which is h = (sqrt(3)/2) times a. To find the side length 'a' we rearrange the formula to a = 2h/sqrt(3) and substitute h = 13 meters to get a = 2 times 13 / sqrt(3). Once we have the side length, we can calculate the perimeter (P) of the triangle by tripling the side length (since all sides are equal in an equilateral triangle), P = 3a.
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