Question

What is the value of x?

Answer 1

`x=4`

Explanation:

We have the triangle `RST` as a `30-60-90` right triangle. We know in such triangles that if the shorter leg has length `a` then the longer leg has length `asqrt3` and hypotenuse has length `2a`.

In `RST`, the longer leg has length `2sqrt3`. From this, we can conclude that `a` is 2 and that the hypotenuse, `RT` has length `4`.

We also have the triangle `RTQ` as a `45-45-90` right triangle with `RT=RQ`. We know from these triangles that the non-hypotenuse lengths are the same side. Since `RT=4`, `RQ=x=4`.