Answer:
√3/1
Step-by-step explanation:
You already know that the side is 2x, so we know that the fraction is the height divided by 2x. Now we need to find the length of the height. There is a theorem that states that the height of an equilateral triangle is x√3/2, if x is the length of a side. However, since our side length is 2x, the height will be 2x√3/2.
The ratio will be 2x√3/2/2x. Since we do not want a fraction inside of a fraction, we have to multiply the numerator and denominator by two to get rid of the denominator in the numerator (I'm sorry if this is confusing, but that's geometry for you). Once we do just that, the ratio will become 4x√3/4x. However, it turns out that we can simplify this even more by reducing the fraction by 4x. The simplified ratio will become √3/1.
The ratio of the height to a side is [tex]\sqrt{3} :1[/tex] and this can be determined by using the Pythagorean theorem.
Given :
The triangle in the figure is equilateral with each side of length 2x.
The ratio of the height to a side can be determined by using the Pythagorean theorem. The Pythagorean theorem is given by the equation:
[tex]\rm H^2=B^2+P^2[/tex]
where H is the hypotenuse, B is the base, and P is the perpendicular.
Applying Pythagorean theorem for triangle ABD.
[tex]\rm (2x)^2=(Height)+x^2[/tex]
[tex]\rm Height =\sqrt{ 4x^2 -x^2}[/tex]
[tex]\rm Height = x\sqrt{3}[/tex]
So, the ratio of the height to a side is [tex]\sqrt{3} :1[/tex].
For more information, refer to the link given below:
https://brainly.com/question/16426393
