Answer:
[tex]y = 6\\\\x = 6\sqrt{2}\\x=8.485[/tex]
Step-by-step explanation:
The base-angles converse theorem states that in a triangle where two angles are congruent, the sides opposite the congruent angles are congruent. One can apply this theorem to the given triangle, and thus, y = 6, because of the base angles converse theorem.
It is also given that the given triangle is a right triangle, therefore, the isosceles triangle with a right angle theorem is applicable. This theorem states that in a right triangle (a triangle with a right angle), that is isosceles (two sides are congruent), the third side (non-congruent side) is equal to the length of the two congruent sides times the square root of (2). Hence, x = [tex]6\sqrt{2}[/tex], in the decimal form that is 8.485.
