 Welcome, geometry students to our third short video on 45-45-90 right triangles, and in our first example in the upper left we have a triangle where we have x and x and x root 2. So to find x we have to solve x root 2, the hypotenuse is equal to 6, so if we divide both sides by the square root of 2 we will get x equals 6 over root 2. Now you should remember from your algebra one days you cannot have a square root on the bottom, so you multiply the top and bottom by the same thing and you would get x equals 6 root 2 over 2. The square root of 2 times the square root of 2 is the square root of 4, which becomes 2 and notice the square root sign is gone. Your final step is to simplify the two numbers outside the radical, 6 over 2 is the same as 3 over 1, so your final answer is 3 root 2. Now for example 2 over here on the upper right we have x, x and x root 2 again to solve for our sides and in this case x would be the same as 3 root 2, so we have x equals 3 root 2 and now y would equal x root 2 which would be 3 root 2 root 2 and to simplify that you take 3 times 2 because the square root of 2 times the square root of 2 is the square root of 4 which is 2 and therefore y would equal 6 and there's more examples of your 45, 45 right triangle.