Question 218860: a right triangle has sides whose lengths are consecutive integers. Find the lengths of the sides.
i dont know how to find the lengths of the sides.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First a definition: Consecutive integers are simply whole numbers that follow one another. Example: 1, 2, 3, 4, 5, 6, etc are consecutive integers.
In general, the terms x, x+1, x+2, x+3, x+4, ... are consecutive integers (where 'x' is a whole number).
Since we're given that "a right triangle has sides whose lengths are consecutive integers", we're basically told that  ,  , and  where 'a' and 'b' are the legs of the triangle and 'c' is the hypotenuse.
Now remember that we can relate the sides of a triangle using the Pythagorean theorem: 
Just plug in the values of 'a', 'b', and 'c' to get: 
 FOIL
 Get everything to one side.
 Combine like terms.
From here, just use the quadratic formula or factor to find 'x'. I'll let you do that.
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