Question 218860
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 {{{a=x}}}, {{{b=x+1}}}, and {{{c=x+2}}} 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: {{{a^2+b^2=c^2}}}



Just plug in the values of 'a', 'b', and 'c' to get: {{{x^2+(x+1)^2=(x+2)^2}}}



{{{x^2+x^2+2x+1=x^2+4x+4}}} FOIL



{{{x^2+x^2+2x+1-x^2-4x-4=0}}} Get everything to one side.



{{{x^2-2x-3=0}}} Combine like terms.



From here, just use the quadratic formula or factor to find 'x'. I'll let you do that.