Question

find the value of $x$. leave your answer in simplest radical form.
answer
$x = $

Explanation:

Step1: Find base of top triangle

Use Pythagorean theorem for right triangle:
$$c^2 = a^2 + b^2$$
Let base be $b$, $a=2$, $b=2$, so:
$$b^2 = 2^2 + 2^2 = 4 + 4 = 8$$
$$b = \sqrt{8} = 2\sqrt{2}$$

Step2: Find $x$ using rectangle diagonal

For rectangle, diagonal $d=5$, side $b=2\sqrt{2}$. Use Pythagorean theorem:
$$x^2 + (2\sqrt{2})^2 = 5^2$$
$$x^2 + 8 = 25$$
$$x^2 = 25 - 8 = 17$$
$$x = \sqrt{17}$$

Answer:

$\sqrt{17}$