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##