What is the value of x? show all of your work.

The Pythagorean Theorem states that the hypotenuse of a right triangle is equal to the square root of the sum of its squared sides, mathematically:

h^2=x^2+y^2, where h=hypotenuse and x and y are the side lengths.

In this case we can say:

(√117)^2=6^2+x^2

117=36+x^2

x^2=117-36

x^2=81

x=√81  since x>0

x=9 cm