Question

the figure below is a square. find the length of side $x$ to the nearest tenth.
(the figure is a square with one side labeled \\(\sqrt{7}\\) and a diagonal labeled $x$)

Explanation:

Step1: Apply Pythagorean theorem

The diagonal $x$ of a square with side length $s$ follows $x^2 = s^2 + s^2$, where $s=\sqrt{7}$.
$x^2 = (\sqrt{7})^2 + (\sqrt{7})^2$

Step2: Simplify the right-hand side

Calculate the squared terms and sum them.
$x^2 = 7 + 7 = 14$

Step3: Solve for x

Take the square root of both sides.
$x = \sqrt{14} \approx 3.7417$

Step4: Round to nearest tenth

Round the decimal to one decimal place.
$x \approx 3.7$

Answer:

3.7