Answer:
[tex] x = 3\sqrt{2} [/tex]
[tex] y = 6\sqrt{2} [/tex]
Step-by-step explanation:
The triangle is a 30-60-90 right triangle.
The ratio of the lengths of the sides is:
[tex] 1 : \sqrt{3} : 2 [/tex]
The order of the sides in the ratio above is
short leg : long leg : hypotenuse
The long leg is sqrt(3) times the length of the short leg.
[tex] x \times \sqrt{3} = 3\sqrt{6} [/tex]
[tex] x = \dfrac{3\sqrt{6}}{\sqrt{3}} [/tex]
[tex] x = 3 \times \sqrt{\dfrac{6}{3}} [/tex]
[tex] x = 3\sqrt{2} [/tex]
The hypotenuse is twice the length of the short leg.
[tex] y = 2 \times 3\sqrt{2} [/tex]
[tex] y = 6\sqrt{2} [/tex]
