Answer
$p=15$
$r= 15\sqrt 2$
$q=5\sqrt 6$
$t=10\sqrt 6$
Work Step by Step
The reference triangles provide ratios of the sides. As we start with the hypotenuse of a 30-60-90 triangle, we can determine its other tow sides. After, we use the ratios of a 45-45-90 triangle.
$p=15$
$r = p\sqrt 2$
$r= 15\sqrt 2$
$q=\frac{r}{\sqrt 3}=\frac{15 \sqrt 2}{\sqrt 3}=5\sqrt 6$
$t=2q$
$t=10\sqrt 6$
