## Elementary Geometry for College Students (5th Edition)

The slant height is $3\sqrt 5$ cm.
Use the Pythagoras Theorem to solve for slant height (variable $x$): $a^{2} + b^{2} = c^{2}$ When $c = x =$ hypotenuse of the right angled triangle 1. Substitute the $a$ and $b$ values to solve for $x$ into the equation $(\sqrt 6)^{2} + (\sqrt 3)^{2} = (\sqrt x)^{2}$ $36 + 9 = x^{2}$ $45 = x^{2}$ $\sqrt 45 = x$ $3\sqrt 5 = x$ Therefore $x = 3\sqrt 5$ cm