## Algebra: A Combined Approach (4th Edition)

$5\sqrt{7} \text{ } cm \text{ OR } \approx 13.2 \text{ } cm$
$\bf{\text{Solution Outline:}}$ Use the Pythagorean Theorem to solve for the value of the missing side measurement. $\bf{\text{Solution Details:}}$ Based on the given figure, the missing side is the hypotenuse, $c,$ of the right triangle. Using the Pythagorean Theorem which is given by $c^=a^2+b^2,$ with $a= 5\sqrt{3}$ and $b= 10 ,$ then \begin{array}{l}\require{cancel} c^2=(5\sqrt{3})^2+10^2 \\\\ c^2=25(3)+100 \\\\ c^2=75+100 \\\\ c^2=175 .\end{array} Taking the principal square root of both sides (since there are no negative side measurement) and simplifying the radical result to \begin{array}{l}\require{cancel} c=\sqrt{175} \\\\ c=\sqrt{25\cdot7} \\\\ c=\sqrt{(5)^2\cdot7} \\\\ c=5\sqrt{7} .\end{array} Hence, the missing side is $5\sqrt{7} \text{ } cm \text{ OR } \approx 13.2 \text{ } cm .$