The height of a parallelogram is 10 feet more than its base. If the area of the parallelogram is 120 square feet, find its base and height.
To find the base and height of a parallelogram, we can use the formula for the area of a parallelogram: Area = base * height.
Given that the area is 120 square feet, we can set up the equation:
120 = base * height.
We are also given that the height is 10 feet more than the base, so we can express the height in terms of the base as:
height = base + 10.
Substituting this expression into the equation for the area, we have:
120 = base * (base + 10).
Now, we can solve this quadratic equation to find the values of the base and height.
Expanding the equation:
120 = base^2 + 10base.
Rearranging the equation:
base^2 + 10base - 120 = 0.
Now, we have a quadratic equation:
(base + 15)(base - 8) = 0.
Setting each factor equal to zero:
base + 15 = 0 or base - 8 = 0.
Solving each equation:
base = -15 or base = 8.
Since the length cannot be negative, we discard the value of -15.
Therefore, the base of the parallelogram is 8 feet.
Using the height equation, we can find the height by substituting the value of the base:
height = base + 10 = 8 + 10 = 18.
Therefore, the base of the parallelogram is 8 feet and the height is 18 feet.