An observation tower's shadow is 9 yards long, Not far away, a plum tree's shadow is 3 yards long, If the observation tower is 12 yards tall, how tall is the plum tree? Write your answer as a whole number or a decimal, Do not round,

To find the height of the plum tree, we can use the concept of similar triangles. The ratio of the heights to the lengths of the shadows will be the same for both the observation tower and the plum tree. So we can set up the equation: \[ \frac{\text{Height of Tower}}{\text{Shadow of Tower}} = \frac{\text{Height of Plum Tree}}{\text{Shadow of Plum Tree}} \] Plugging in the values we have: \[ \frac{12 \text{ yards}}{9 \text{ yards}} = \frac{\text{Height of Plum Tree}}{3 \text{ yards}} \] Cross-multiplying gives us: \[ 12 \text{ yards} \times 3 \text{ yards} = 9 \text{ yards} \times \text{Height of Plum Tree} \] This simplifies to: \[ 36 = 9 \times \text{Height of Plum Tree} \] Dividing both sides by 9: \[ \text{Height of Plum Tree} = 4 \text{ yards} \] Thus, the plum tree is 4 yards tall.