SOLUTION: An equilateral triangle has sides of 14, what is the measure of the altitude?

Question 545891: An equilateral triangle has sides of 14, what is the measure of the altitude?
Answer by Student A(4) (Show Source): You can put this solution on YOUR website!
By using the Pythagorean theorem one can solve this question. The altitude extends from the vertex of the triangle to the midpoint of the base forming a right angle at the base and thus two right triangles. The Pythagorean theorem states that in a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. So being an equilateral triangle all sides are equal to 14. The side opposite the right angle is the hypotenuse and it is 14 squared. We want to find the altitude which is one of the sides, let's call it x. The other side would be from the midpoint to one of the end points. So it's length would be half of the length of the base 14/2 = 7
=> 7^2 + x^2 = 14^2 => 49 + x^2 = 196 => x^2 = 147 => x = sqrt 147 = 7 * sqrt 3 . So the altitude is equal to 7 * sqrt 3. An approximate value to that would be 12.12
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