## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$5\sqrt{2} \text{ } cm$
The diagonal and 2 sides of the square form a right triangle. Let $c$ be the hypotenuse and $a,b$ be the equal legs. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, where $c=10$ and $a=b,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ a^2+a^2=10^2 \\\\ 2a^2=100 \\\\ a^2=\dfrac{100}{2} \\\\ a^2=50 \\\\ a=\sqrt{50} \\\\ a=\sqrt{25\cdot2} \\\\ a=\sqrt{(5)^2\cdot2} \\\\ a=5\sqrt{2} .\end{array} Hence, the side of the square (which has the same value as the legs) is equal to $5\sqrt{2} \text{ } cm .$