10) A 12 foot tall monurnert has a shadow that is 9 feet long. A nearby water tower has a shadow that is 12 feet long. How tall is the water tower? \( \begin{array}{llll}\text { A) } 18 \text { feet } & \text { B) } 24 \text { feet } & \text { C) } 25.3 \text { feet } & \text { D) } 16 \text { feet }\end{array} \)

To find the height of the water tower, we can use the concept of similar triangles. The height of the monument and its shadow form one triangle, and the height of the water tower and its shadow form another triangle. Let \( h \) be the height of the water tower. We can set up a proportion based on the heights and shadows: \[ \frac{\text{Height of monument}}{\text{Shadow of monument}} = \frac{\text{Height of water tower}}{\text{Shadow of water tower}} \] Substituting the known values: \[ \frac{12 \text{ feet}}{9 \text{ feet}} = \frac{h}{12 \text{ feet}} \] Now, we can cross-multiply to solve for \( h \): \[ 12 \text{ feet} \cdot 12 \text{ feet} = 9 \text{ feet} \cdot h \] \[ 144 = 9h \] Now, divide both sides by 9: \[ h = \frac{144}{9} = 16 \text{ feet} \] Thus, the height of the water tower is \( \boxed{16} \) feet.