the figure below is a square. find the length of side $x$ in simplest radical form with a rational…
the figure below is a square. find the length of side $x$ in simplest radical form with a rational denominator.
Answer
Explanation:
Step1: Recall Pythagorean theorem for square
In a square with side length $a$ and diagonal $d$, $d^{2}=a^{2}+a^{2}=2a^{2}$. Here $a = \sqrt{8}$ and $d=x$.
Step2: Substitute values into the formula
$x^{2}=(\sqrt{8})^{2}+(\sqrt{8})^{2}$. Since $(\sqrt{8})^{2}=8$, then $x^{2}=8 + 8=16$.
Step3: Solve for $x$
$x=\sqrt{16}=4$.
Answer:
$4$