Question

The height of a parallelogram is 5 feet more than it's base. If the area of the parallelogram is 204 square feet, what is its base and height?

Answer 1

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.

$x(x+5)=204 \\ x^2+5x=204 \\ x^2+5x-204=0 \\ x^2+17x-12x-204=0 \\ x(x+17)-12(x+17)=0 \\ (x-12)(x+17)=0 \\ x-12=0 \ \lor \ x+17=0 \\ x=12 \ \lor \ x=-17$

The length of the base of a parallelogram must be a positive number, so x=12.

$\hbox{the base:} \\ x=12 \\ \\ \hbox{the height:} \\ x+5=12+5=17$

The base is 12 feet long, the height is 17 feet long.