Suppose that the correct answer is $n$ and David's answer is $d$. Note that the volume of the prism is directly proportional to $Hh^2$. Since we only care about the ratio, the answer is $$\frac{n}{d}=\frac{15\cdot 6^2}{6\cdot 15^2}=\boxed{\frac{2}{5}}.$$

shouldn't it be $1$

Iwowowl253 wrote: shouldn't it be $1$ that was my answer too

If he knows the length of the sides of the triangle, $s$, and use the formula $V=\frac{1}{2}hsH$ then it doesn't matter if $h$ and $H$ are switched. Rightly using $h$ to calculate $s$ we get $s=4\sqrt{3}$ and $V=180\sqrt{3}$ Using $H$ to calculate $s$ we get $s=10\sqrt{3}$ and $V=450\sqrt{3}$ Therefore the ratio is $\frac{2}{5}$

oh yeah idk why i assumed he knew the length of the side of the triangle