Question

Find the value of x and the value of y

Answer 1

The triangle is an isosceles triangle with exactly two congruent angles.
Since the two 45-deg angles are congruent, their opposite sides are also congruent. That makes y = 5.

This triangle is a 45-45-90 triangle. In a 45-45-90 triangle, the legs are congruent and the hypotenuse is sqrt(2) times the length of the legs.
The hypotenuse has length x, so x = 5 * sqrt(2) = 5sqrt(2)

Answer: B. x = 5sqrt(2), y = 5