Question

1. a 12 - inch tall model casts a shadow of 4 inches. a full - scale object casts a shadow of 16 feet. how tall is the full - scale object? a. 36 feet b. 64 feet c. 46 feet d. 48 feet

Explanation:

Step1: Set up proportion

Let $x$ be the height of the full - scale object. The ratio of the height to the shadow length of the model is the same as the ratio of the height to the shadow length of the full - scale object. The model's height is 12 inches and its shadow is 4 inches. The full - scale object's shadow is 16 feet (first convert all units to the same, 12 inches = 1 foot, 4 inches=$\frac{4}{12}=\frac{1}{3}$ foot, 16 feet). The proportion is $\frac{1}{\frac{1}{3}}=\frac{x}{16}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{1}{\frac{1}{3}}=\frac{x}{16}$ gives $x\times\frac{1}{3}=1\times16$.

Step3: Solve for $x$

Multiply both sides of the equation $x\times\frac{1}{3}=16$ by 3 to get $x = 48$ feet.

Answer:

d. 48 feet