Determine the length of one of the bases of a trapezoid if the area of the trapezoid is 510.0 square feet. The height is 20.0 feet and one of the bases is 14.0 feet.
The area of a trapezoid is given by the formula:
Area = (1/2) * (sum of the bases) * height
In this case, we are given the area (510.0 square feet), the height (20.0 feet), and one of the bases (14.0 feet).
Let's denote the other base as x.
The formula becomes:
510.0 = (1/2) * (14.0 + x) * 20.0
Now we can solve for x:
1020.0 = (14.0 + x) * 20.0
Divide both sides by 20.0:
51.0 = 14.0 + x
Subtract 14.0 from both sides:
51.0 - 14.0 = x
37.0 = x
Therefore, the length of the other base is 37.0 feet.