The area of a parallelogram is Area = (Base)(Height)
Let's label the height "H" and the base "B"
It is given that the base is 4 units longer than the height, so B = H + 4
Now we can plug this into the formula for Area to create an equation with only 1 unknown.
Note that the Area is given to be 45
Area = (Base)(Height) = (H + 4)(H) = 45
Now let's solve for H.
(H + 4)(H) = 45
H^2 + 4H = 45
H^2 + 4H - 45 = 0
(H + 9)(H - 5) = 0
So, H = -9 or H = 5
Since the height H cannot be negative, it must be 5.
Now we can plug this into the equation for the base to find it's length,
B = H + 4 = 5 + 4 = 9
Therefore, the base of the parallelogram is 9 units long.
