Question

Find the value of x and the value of y.​

Answer 1

`x=7,\\y=4√(2)`

Explanation:

Draw an auxiliary line in the trapezoid forming a triangle and a rectangle. The dimensions of the rectangle are 3 x 4, so the length of the auxiliary line must be 4.

The auxiliary line also creates a 45-45-90 triangle. The auxiliary line itself makes up one leg of the triangle, and since we know it is 4, we can use the Pythagorean Theorem to find y:

`4^2+4^2=y^2,\\y^2=32,\\y=√(32)=\boxed{4√(2)}`

The length of x can be found by adding the bottom leg of the 45-45-90 triangle and the bottom dimension of the rectangle:

`x=4+3=\boxed{7}`