The triangle below is equilateral. Find the length of side x in simplest radical form with a rational denominator.
x
√10
To find the length of side x in simplest radical form with a rational denominator, we can use the Pythagorean theorem.
Since the triangle is equilateral, we know that all three sides are equal. Let the length of each side be a.
By the Pythagorean theorem applied to the triangle, we have:
(x/2)^2 + a^2 = a^2
Solving for a:
(x/2)^2 + a^2 = a^2
x^2/4 + a^2 = a^2
x^2/4 = 0
x^2 = 0
x = √10
Therefore, the length of side x in simplest radical form with a rational denominator is √10.