An equilateral triangle has an altitude of 15m. What is the perimeter of the triangle?
The answer is 30 * sqrt 3 m
To find the perimeter of an equilateral triangle, we first need to determine the length of one side.
In an equilateral triangle, all three sides are equal in length. Let's call the length of each side 's'.
The altitude of the equilateral triangle bisects the base into two equal segments, forming a right triangle with the altitude as the hypotenuse.
Using the Pythagorean theorem, we can find the length of each half of the base:
c^2 = a^2 + b^2
where 'a' and 'b' are the two equal segments of the base, and 'c' is the altitude.
In this case, the altitude is 15m, so we have:
c^2 = (s/2)^2 + 15^2
= s^2/4 + 225
Since the triangle is equilateral, all sides have the same length, so we can use any side length, 's'.
Now, we'll use the formula to find the area of an equilateral triangle:
A = (s^2√3)/4
Knowing that the area is given by 150m², and isolating 's' in the area formula, we can solve for 's':
150 = (s^2√3)/4
(s^2√3)/4 = 150
s^2√3 = 600
s^2 = 600 / √3
To calculate the perimeter, we simply multiply the length of one side by 3:
Perimeter = 3s
Now, let's substitute the value of 's' into the perimeter equation:
Perimeter = 3 * √(600 / √3)
By simplifying this expression, we can find the perimeter of the equilateral triangle.
Reiny has worked a similar problem.
http://www.jiskha.com/display.cgi?id=1298504109