 Welcome geometry students to special right triangles examples. These three examples are for 45 45 90-degree triangles and Our shortcut and rule you need to remember and memorize is that the two legs are always going to be the same And we're going to label those x and x so on the first triangle up or left I'm going to make the 5 and x and We already have an x on this side and the third side is x root 2 so in this case 5 is equal to x so we're going to have x equals 5 and Our y is going to be equal to x root 2 which would be 5 root 2 Now for the second example in the upper right x and x are already labeled the hypotenuse would be labeled with x root 2 So you can see that x is equal to 8 and So if you're giving given something in the form of x and x and x root 2 It's quite simple to do a 45 45 degree triangle now our third and final example is going to be one of our harder ones because we've got x and x and 6 is on the x root 2 side So we actually have to solve x root 2 equals 6 So if you divide both sides by root 2 you get x equals 6 over root 2 Now if you remember from radicals you cannot have a square root on the bottom of a fraction So we need to multiply the top and bottom by the square root of 2 when we do that We get x equals 6 root 2 Over the square root of 2 times the square root of 2 which is a square root of 4 which is 2 To finish this problem. You can simplify 6 over 2 by division and they are the same as 3 Over 1 so your final answer would be 3 root 2 over 1 which is 3 root 2