Answer
The length of the base is 17 feet.
Work Step by Step
Let $x$ feet be the length of the base.
Since the length of the base of the triangle is 9 feet longer than its height, the height = $x - 9$.
Area of triangle = $\frac{(Base)(Height)}{2}$
68 = $\frac{x(x - 9)}{2}$
$x^2 - 9x - 136 = 0$
$(x - 17)(x + 8) = 0$
$x = 17$ or $x = -8$ (rejected)
Therefore, x = 17, and the length of the base is 17 feet.
