Write the equation of the conic section shown below. (Its a triangle)
√10
Sorry, it is not possible to write the equation of a triangle as a conic section. Conic sections are curves that result from intersecting a cone with a plane, and triangles are not curves. Can you provide more information about the context or shape you are referring to?
The triangle below is equilateral. Find the length of the side x in simplest radical form with a rational denominator.
√10
If the triangle is equilateral, then all sides have the same length. Let's call that length "s".
Using the Pythagorean theorem on one of the right triangles formed by cutting the equilateral triangle in half, we have:
(s/2)^2 + x^2 = s^2
Simplifying this equation:
s^2/4 + x^2 = s^2
x^2 = s^2 - s^2/4 = 3s^2/4
x = sqrt(3s^2/4) = (sqrt(3)/2) s
We know that the length of one side is √10. Setting √10 = (sqrt(3)/2) s and solving for s, we get:
s = (2/sqrt(3)) √10 = (2/3) sqrt(30)
Now we can plug this value of s into the equation we found earlier for x:
x = (sqrt(3)/2) s = (sqrt(3)/2) (2/3) sqrt(30) = sqrt(10/3) = (sqrt(30)/3)
Find the length of side x in simplest radical form with a rational denominator.
7
More information is needed to solve this problem. Please provide a diagram or additional context.
Find the length of side x in simplest radical form with a rational denominator.
√7
More information is needed to solve this problem. Please provide a diagram or additional context.
Find the length of side x in simplest radical form with a rational denominator.
one side = 7