An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle?
(1 point)
Responses
30square root of 2 m
30 Image with alt text: square root of 2 m
45 m
45 m
30square root of 3 m
30 Image with alt text: square root of 3 m
60square root of 3 m
The perimeter of an equilateral triangle can be found by multiplying the length of one side by 3.
In this case, since the triangle has an altitude of 15 m, the altitude is also the height of the equilateral triangle.
To find the length of one side of the triangle, we can use the Pythagorean theorem. The altitude divides the equilateral triangle into two right-angled triangles, each with a base equal to half of one side of the triangle.
Using the Pythagorean theorem, we have:
(1/2 side)^2 + 15^2 = side^2
(1/4 side^2) + 225 = side^2
225 = side^2 - (1/4 side^2)
225 = (3/4) side^2
300 = side^2
side = sqrt(300) = 10 sqrt(3)
Therefore, the perimeter of the equilateral triangle is:
perimeter = 3 * side = 3 * 10 sqrt(3) = 30 sqrt(3) m
The correct answer is option:
30 sqrt(3) m