Question

find the length of the third side. if necessary, write in simplest radical form.
(image of a right triangle with legs 2√3 and 2)

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown side be $c$. For a right triangle, $c^2 = a^2 + b^2$, where $a=2$, $b=2\sqrt{3}$.
$$c^2 = 2^2 + (2\sqrt{3})^2$$

Step2: Calculate each term

$$c^2 = 4 + (4\times3) = 4 + 12$$

Step3: Sum and take square root

$$c^2 = 16 \implies c = \sqrt{16}$$

Answer:

$4$