If an equilateral triangle has an altitude of 4.12 cm, how many cm long is one of its sides?
If the length of one of its sides is x.
Then x/2 is half the side.
An altitude divides the equilateral triangle into two congruent right triangles, each with half of one side (x/2) as the short side, the altitude as the long side, and the side (x) as the hypotenuse.
So by using Pythagoras Theorem, we have
(x/2)² + 4.12²= x²
Solve for x.
Thank you!
You're welcome!
To find the length of one side of an equilateral triangle, we can use the altitude, which is the perpendicular distance from the base to the opposite vertex.
In an equilateral triangle, the altitude bisects both the base and the opposite side, creating two congruent right triangles. Let's label the length of one side of the triangle as "s".
Using the Pythagorean theorem, we can find the length of the altitude:
altitude^2 = (1/2 * s)^2 + s^2
4.12^2 = (1/2 * s)^2 + s^2
16.9744 = (1/4 * s^2) + s^2
16.9744 = (1/4 + 1) * s^2
16.9744 = (5/4) * s^2
s^2 = (16.9744 * 4) / 5
s^2 = 13.57952
s = √13.57952
s ≈ 3.68 cm
Therefore, one side of the equilateral triangle is approximately 3.68 cm long.