Question

the triangle below is equilateral. find the length of side $x$ in simplest radical form with a rational denominator. $sqrt{11}$
answer attempt 1 out of 2
$x = $

Explanation:

Step1: Define triangle side length

Let each side of the equilateral triangle be $s = \sqrt{11}$.

Step2: Use 30-60-90 triangle ratios

The altitude $x$ of an equilateral triangle is $\frac{\sqrt{3}}{2}$ times the side length.
$$x = \frac{\sqrt{3}}{2} \times s$$

Step3: Substitute side length value

$$x = \frac{\sqrt{3}}{2} \times \sqrt{11}$$

Step4: Simplify the expression

$$x = \frac{\sqrt{33}}{2}$$

Answer:

$\frac{\sqrt{33}}{2}$