The base is x.
The height is 5 feet more than the base, so it's x+5.
The area of a parallelogram is the product of its base and its height. The area is 204 square feet.
[tex]x(x+5)=204 \\
x^2+5x=204 \\
x^2+5x-204=0 \\
x^2+17x-12x-204=0 \\
x(x+17)-12(x+17)=0 \\
(x-12)(x+17)=0 \\
x-12=0 \ \lor \ x+17=0 \\
x=12 \ \lor \ x=-17[/tex]
The length of the base of a parallelogram must be a positive number, so x=12.
[tex]\hbox{the base:} \\ x=12 \\ \\
\hbox{the height:} \\ x+5=12+5=17[/tex]
The base is 12 feet long, the height is 17 feet long.
