Question 76200
let x=length of hypotenuse...so one leg is x-9 and the other is x-2


by Pythagoras {{{(x-9)^2+(x-2)^2=x^2}}}...expanding gives {{{x^2-18x+81+x^2-4x+4=x^2}}}


rearranging and combining terms gives...{{{x^2-22x+85=0}}}...factoring gives (x-17)(x-5)=0...so x=17 or x=5


since 5-9 gives a negative result, the length of the hypotenuse is 17 centimeters