An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle?
(1 point)
30\sqrt{2}m
45 m
30\sqrt{3}m
60\sqrt{3}m
In an equilateral triangle, the altitude also serves as the perpendicular bisector of the base. Therefore, the base is divided into two congruent segments, each with a length of 15 m/2 = 7.5 m.
Using the Pythagorean theorem, we can find the length of the side of the equilateral triangle:
(side length)^2 = (base/2)^2 + altitude^2
(side length)^2 = (7.5 m)^2 + (15 m)^2
(side length)^2 = 56.25 m^2 + 225 m^2
(side length)^2 = 281.25 m^2
side length ≈ √281.25 m ≈ 16.77 m
Since an equilateral triangle has three congruent sides, the perimeter of the triangle is 3 * side length = 3 * 16.77 m = 50.31 m ≈ 45 m.
Therefore, the correct answer is 45 m.