A Rectangle Has A Diagonal That Measures 10 Centimeters And A Length That Is 2 Centimeters Longer Than The Width. What Is The Width Of The Rectangle In Centimeters?

We can use Pythagorean Theorem.
10^2=(x+2)^2 + x^2.
Then
100=x^2+4x+4+x^2
100=2x^2+4x+4
50=x^2+2x+2
0=x^2+2x-48
then factor

x=6 or x=-8
It cannot be negative since it's a measure of width.
Therefore x=6.