Answer:
[tex]n=\dfrac{9}{2}[/tex]
[tex]m=9[/tex]
Step-by-step explanation:
We can solve for the unknown side lengths of the right triangle using the ratio of sides in a 30-60-90 triangle:
[tex]A \ :\ A\sqrt3\ : \ 2A[/tex]
We are given that:
[tex]A\sqrt3 = \dfrac{9\sqrt3}{2}[/tex]
↓ dividing both sides by [tex]\sqrt3[/tex]
[tex]\boxed{A =\dfrac{9}{2} = n}[/tex]
___
[tex]m = 2A[/tex]
↓ plugging in [tex]A = 9/2[/tex]
[tex]m = 2\left(\dfrac{9}{2}\right)[/tex]
[tex]\boxed{m = 9}[/tex]
