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

$3\sqrt{3}$
The given triangle is an equilateral triangle. In an equilateral triangle the height bisects the base into two equal parts. Hence, a right triangle is formed where one of the legs is $3$ units and the hypotenuse is $6$ units. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $a=3$ and $c=6 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ 3^2+b^2=6^2 \\\\ 9+b^2=36 \\\\ b^2=36-9 \\\\ b^2=27 \\\\ b=\sqrt{27} \\\\ b=\sqrt{9\cdot3} \\\\ b=\sqrt{(3)^2\cdot3} \\\\ b=3\sqrt{3} .\end{array} Hence, the missing side measures $3\sqrt{3}$ units.