Question

the three sides of a right triangle are consecutive even integers. what is the length of each side?

Answer 1

side 1 = x (hypt.)
side 2 = x + 2
side 3 = x + 4

(x + 2)^2 + (x + 4)^2 = x^2
x^2 + 4x + 4 + x^2 + 8x + 16 = x^2
x^2 + 12x + 20 = 0
(x + 10)(x + 2) = 0

i'm not sure why i ended up with negatives...but we can say that since this is length it has to be positive
so you have 10 and 2 as your answer
but since we said that 10 is the hypt. it has to be the longest side. so it must be 10
so the sides are 6, 8, and 10

Answer 2

\[(x-2)^2+x^2=(x+2)^2\]
\[x^2-4x+4+x^2=x^2+4x+4\]
\[x\cdot(x-8)=0\]
x=8
sides: 6 ,8 ,10