A billboard is 12 meters tall and its shadow is 16 meters long. A nearby totem pole is 9 meters tall. How long is the totem pole's shadow? Write your answer as a whole number or a decimal. Do not round. meters

To determine the length of the totem pole's shadow, we can use the concept of similar triangles. The heights of the objects and the lengths of their shadows form proportional relationships. Given: - **Billboard:** - Height = 12 meters - Shadow length = 16 meters - **Totem Pole:** - Height = 9 meters - Shadow length = \( x \) meters Set up the proportion based on the heights and shadow lengths: \[ \frac{\text{Height of Billboard}}{\text{Shadow of Billboard}} = \frac{\text{Height of Totem Pole}}{\text{Shadow of Totem Pole}} \] Substitute the known values: \[ \frac{12}{16} = \frac{9}{x} \] Simplify the fraction: \[ \frac{3}{4} = \frac{9}{x} \] Solve for \( x \) by cross-multiplying: \[ 3x = 36 \] \[ x = 12 \] **The totem pole's shadow is 12 meters long.** **Answer:** 12