The lengths of the three sides of a right triangle are given by three consecutive even integers. find the lengths of the three sides.

X²+(x+1)²=(x+2)²
x²+x²+2x+1=x²+4x+4
x²-2x-3=0
(x+1)(x+3)=0
x= -1 or 3
since x cannot be-1 (the length of a triangle side cannot be negative) we conclude x=3 and our side after 3,4,5

it might be helpful to remember in the future that this is the ONLY Pythagorean triple with this property.

incidentally the area of this triangle is the next digit 6!