How would you construct an isosceles right triangle if only given the hypotenuse?

If you know the length of the hypotenuse, you can find the length of the other two sides of the triangle using the Pythagorean theorem (a^2 + b^2 = c^2). However, since this is an isosceles triangle, the two sides will be the same length, so you will simplify the Pythagorean formula to x^2 + x^2 = c^2, or 2x^2 = c^2. For example, if the hypotenuse is 12 cm, the formula will be 2x^2 = 12^2: 2x^2 = 12^2 2x^2 = 144 2x^2/2 = 144/2 x^2 = 72 sqrt*x^2 = sqrt*72 x = 8.48. Since every triangle has 180 degrees, if it is a right triangle, the angle measurements are 90-45-45. So the triangle will have a hypotenuse of 12, two side lengths of about 8.5 cm, and two 45 degree angles.