The triangle below is divided into nine stripes of equal width each parallel to the base of the triangle. The darkened stripes have a total area of $135$. Find the total area of the light colored stripes.
[img]https://cdn.artofproblemsolving.com/attachments/0/8/f34b86ccf50ef3944f5fbfd615a68607f4fadc.png[/img]
1. Let the area of the uppermost strip be \( x \).
2. The areas of the darkened stripes are given as \( x, 5x, 9x, 13x, \) and \( 17x \). This is because the area of each strip increases quadratically as we move down the triangle, due to the similarity of the smaller triangles formed by the strips.
3. The total area of the darkened stripes is:
   \[
   x + 5x + 9x + 13x + 17x = 45x
   \]
4. We are given that the total area of the darkened stripes is \( 135 \). Therefore, we can set up the equation:
   \[
   45x = 135
   \]
5. Solving for \( x \):
   \[
   x = \frac{135}{45} = 3
   \]
6. The areas of the light-colored stripes are \( 2x, 4x, 6x, \) and \( 8x \).
7. The total area of the light-colored stripes is:
   \[
   2x + 4x + 6x + 8x = 20x
   \]
8. Substituting \( x = 3 \) into the equation:
   \[
   20x = 20 \times 3 = 60
   \]

The final answer is \(\boxed{60}\).