This becomes a Tough Nut Challenge! Finding the lengths depends on using the ratio for the sides of a 30-60-90 triangle as the name of the problem suggests. Below the diagrams show how to take the pieces which make a square of unit area and fit the pieces together to make an equilateral triangle of the same area with side 2t and knowing this you can calculate t. The way pieces fit together gives you that p=t and the rest is up to you!

You can calculate the length 't' knowing the area of the equilateral triangle. Pythagoras theorem and the sine rule can be used in finding the other lengths.