What is the area of a rectangle with length (2x+2) width (x) and a diagonal of 13?

The area of such rectangle is ##60##.
Using the ##a^2+b^2=c^2## we substitute the expressions into the equation:
##x^2+(2x+2)^2=13^2##
##x^2+4x^2+8x+4=169##
##5x^2+8x-165=0##
Factor the equation:
##(5x^2-25x)+(33x-165)=0##
##5x(x-5)+33(x-5)=0##
##(5x+33)(x-5)=0##
The two solutions we find are ##-33/5## and ##5##. Since we cannot have a negative width we immediately discard the negative solution leaving us with ##x=5##.
Now we simply solve for the area by substituting ##x## with ##5## and we get our answer:
##2(5)+2=10+2=12##
##5*12=60##