Question

find the value of $x$. leave your answer in simplest radical form.
(image of a figure with a right triangle on top (legs 2 and 2) and a rectangle below with height $x$ and diagonal 5)
answer
attempt 1 out of 2
$x = \square$ submit answer

Explanation:

Step1: Find base of top triangle

Use Pythagorean theorem for right triangle:
$$c^2 = a^2 + b^2$$
Here, $a=2$, $b=2$, let base = $s$:
$$s^2 = 2^2 + 2^2 = 4 + 4 = 8$$
$$s = \sqrt{8} = 2\sqrt{2}$$

Step2: Find $x$ using rectangle diagonal

The diagonal of the rectangle is 5, one side is $s=2\sqrt{2}$, the other is $x$. Apply Pythagorean theorem:
$$x^2 + s^2 = 5^2$$
Substitute $s^2=8$:
$$x^2 + 8 = 25$$

Step3: Solve for $x$

$$x^2 = 25 - 8 = 17$$
$$x = \sqrt{17}$$

Answer:

$\sqrt{17}$