Question

What is the value of x?

Answer 1

Because the two triangles together create another 90 degree angle on the right-most side, we can tell the triangle is a 45-45-90 triangle

So the base of the height (the given value is 3). Because it is a 45-45-90, the height is also 3.

You can now find x by using Pythagorean theorem OR just the proof of a 45-45-90 triangle.

Pythagorean theorem version:

a^2 + b^2 = c^2
3^2 + 3^2 = x^2
9 + 9 = x^2
18 = x^2
x = 3
`√(2)`

45-45-90 proof

The legs of a 45-45-90 triangle are congruent so you just take the value of a leg and place a
`√(2)` at the end of it.

Leg length is 3 units. Slap a
`√(2)` on the end; answer is 3
`√(2)`