Special Types of Triangles

First one

This is an equilateral triangle....all sides are equal....so....this implies that

2x + 5  =  4x  - 1       add 1 to both sides, subtract 2x from each side

6  = 2x       divide both sides by 2

3  = x

Second one....again...we have an equilateral triangle...so...

5x  - 4  = 3x      add 4 to both sides....subtract 3x from both sides   

2x  = 4   divide both sides by 2

x  = 2

So  AB  =  5(2) - 4   =  6

Third one.....this is  a 30-60-90  right triangle....the hypotenuse is opposite the 90 degree angle

And the side oppposite the 30 degree angle is 1/2 of the hypotenuse

So  x  =  (1/2) *8   =  4

Last one.....this is a 45-45-90 right triangle

The side opposite the right angle  - x -  is  √2 times as long as either of the other two sides

So

x  = √2 * 6   =  6√2