An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle? (1 point); 30sqrt(2) m 45 m 30sqrt(3) m 60sqrt(3) m
The altitude of an equilateral triangle splits the triangle into two right triangles. Since the triangle is equilateral, the altitude is also the median and the angle of 60 degrees at the top of the triangle is split into two 30-degree angles by the altitude.
Using trigonometry, we can find that the hypotenuse of each right triangle (which is equal to a side of the equilateral triangle) is equal to 2 * (15/sin(30)) = 30sqrt(3) meters.
Since an equilateral triangle has three equal sides, the perimeter of the triangle is 3 * 30sqrt(3) = 90sqrt(3) meters.
Therefore, the perimeter of the triangle is 90sqrt(3) meters.