SOLUTION: The hypotenuse of a Right Triangle is 9 centemeters longer than one leg and 2 centimeters longer than the other. What is the length of the hypotenuse?

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Question 76200This question is from textbook Algebra II
: The hypotenuse of a Right Triangle is 9 centemeters longer than one leg and 2 centimeters longer than the other. What is the length of the hypotenuse? This question is from textbook Algebra II

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x=length of hypotenuse...so one leg is x-9 and the other is x-2

by Pythagoras %28x-9%29%5E2%2B%28x-2%29%5E2=x%5E2...expanding gives x%5E2-18x%2B81%2Bx%5E2-4x%2B4=x%5E2

rearranging and combining terms gives...x%5E2-22x%2B85=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