SOLUTION: The lengths of the sides of a right triangle are consecutive integers. Find the lengths of the three sides. (I know the answer is 3, 4, and 5 but how do I show the work?)

Algebra ->  Pythagorean-theorem -> SOLUTION: The lengths of the sides of a right triangle are consecutive integers. Find the lengths of the three sides. (I know the answer is 3, 4, and 5 but how do I show the work?)      Log On


   

Question 367760: The lengths of the sides of a right triangle are consecutive integers. Find the lengths of the three sides. (I know the answer is 3, 4, and 5 but how do I show the work?)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Let x represent the shortest side or smallest consecutive integers.

the other side (x+1) and the longest (the hypotenuse) (x + 2)

Appying the Pythagorean Theorem

x^2 + (x+1)^2 = (x+2)^2

x^2 + x^2 +2x + 1 = x^2 + 4x + 4

x^2 -2x -3 = 0

(x-3)(x+1) = 0

(x-3)=0

x = 3, the length of the shortest side

(x+1) = 0

x = -1 cannot use



3 , 4 , 5 are the length of the sides