Question

the figure below is a square. find the length of side $x$ to the nearest tenth.

(figure of a square with a diagonal labeled $x$ and a side labeled 2)

answer attempt 1 out of 2
$x = \square$

Explanation:

Step1: Identify square properties

All sides of the square are length 2. The line $x$ divides the square into two congruent right isosceles triangles, where $x$ is the hypotenuse.

Step2: Apply Pythagorean theorem

For a right triangle with legs $a$ and $b$, hypotenuse $c = \sqrt{a^2 + b^2}$. Here $a = b = 2$.
$$x = \sqrt{2^2 + 2^2}$$

Step3: Calculate and round

Simplify the expression:
$$x = \sqrt{4 + 4} = \sqrt{8} \approx 2.8$$

Answer:

$2.8$