Question

the triangle below is equilateral. find the length of side ( x ) to the nearest tenth.

Explanation:

Step1: Identify right triangle sides

The equilateral triangle has side length 12, so the right triangle has hypotenuse $12$, and one leg is $\frac{12}{2}=6$.

Step2: Apply Pythagorean theorem

Use $a^2 + b^2 = c^2$, solve for $x$:
$$x = \sqrt{12^2 - 6^2}$$

Step3: Calculate and simplify

$$x = \sqrt{144 - 36} = \sqrt{108} = 6\sqrt{3} \approx 10.4$$

Answer:

$10.4$