The base of a parallelogram is 7 ft more than the height. if the area of the parallelogram is 60ft square, what are the measures of the base and the height?

To find the area of a parallelogram, we use the formula:

When we plug in the givens we get:

Distribute the x:

Because we got an , we need to factor the equation.

Turn the equation into standard form by subtracting 60 from both sides:

Now, we can factor this by using the quadratic formula.

Quadratic formula is pure memorizing so I don't like it. But it is very useful because it works all the time. The template for it is: .

When we plug in the values in the standard form we get:

Simplify:







Now, we need to branch out the plus-minus sign:

Because a measurement can't be negative, 5 is the height.

After finding the height, we know that base is so, the base is .

Set up a system of equations