The hypotenuse of a 45°-45°-90° triangle measures 10 sqrt 5 in. what is the length of one leg of the triangle?

There is one rule to remember for 45-45-90 right triangle: hyp = sqrt2 * leg
Given the hypotenuse, plug the value into the equation and solve.

10sqrt5 = sqrt2 * leg
Divide both sides by sqrt2

10sqrt5
  = leg
sqrt2

Multiply the numerator and denominator by sqrt2 to clear the radical..
(10sqrt5)(sqrt2)                          10 sqrt10                        5sqrt10  = leg
  = leg                  = leg            
(sqrt2)(sqrt2)                                    2

Okay so it will be 1123