Question

find the value of x and y

Answer 1

Here we're working with equilateral triangles. Let's start with the triangle containing y: We know both of the legs are of length 3*sqrt(2), so the hypotenuse, y, is found by:
a^2 + b^2 = y^2 =>
(3*sqrt(2))^2 +(3*sqrt(2))^2 = 9*2 + 9*2 = 18 + 18 = 36 = y^2
y = sqrt(36) = 6

The triangle containing x is a right triangle with one 45 degree angle, so we know that it is also an equilateral triangle. We also know that the hypotenuse is of length 3*sqrt(2).
So then:
x^2 + x^2 = 2*x^2 = (3*sqrt(2))^2 = 9*2 = 18
x^2 = 9
x = 3