(9) A plum tree casts a 16 foot long shadow. At the same time, a bamboo plant casts a 4 foot long shadow. If the bamboo plant is 3 feet tall, how tall is the plum tree? \( \begin{array}{llll}\text { A) } 12 \text { feet } & \text { B) } 48 \text { feet } & \text { C) } 21.3 \text { feet } & \text { D) } 16 \text { feet }\end{array} \)

To find the height of the plum tree, we can use the concept of similar triangles. The ratio of the height of the plant to the length of its shadow will be the same for both the bamboo plant and the plum tree. Let \( h \) be the height of the plum tree. We know the following: - The height of the bamboo plant is 3 feet, and its shadow is 4 feet. - The shadow of the plum tree is 16 feet. We can set up the proportion: \[ \frac{\text{Height of bamboo}}{\text{Shadow of bamboo}} = \frac{\text{Height of plum tree}}{\text{Shadow of plum tree}} \] Substituting the known values: \[ \frac{3 \text{ feet}}{4 \text{ feet}} = \frac{h}{16 \text{ feet}} \] Now, we can cross-multiply to solve for \( h \): \[ 3 \times 16 = 4 \times h \] \[ 48 = 4h \] Now, divide both sides by 4: \[ h = \frac{48}{4} = 12 \text{ feet} \] Thus, the height of the plum tree is \( \boxed{12} \) feet.