Question

1. models: an airplane has a wingspan of 25 ft and a length of 20 ft. you are designing a model of the airplane with a wingspan of 15 in. what will the length of your model be? 19) projections: you project a drawing 7 inches wide and 4.5 inches tall onto the wall. the projected image is 27 inches tall. how wide is the projected image?

Explanation:

18)

Step1: Set up the proportion

Since the model and the actual airplane are similar, the ratios of their corresponding dimensions are equal. Let \(x\) be the length of the model (in inches). First, convert the actual airplane's wingspan from feet to inches. \(25\ ft=25\times12 = 300\) inches and the actual length is \(20\ ft = 20\times12=240\) inches. The proportion is \(\frac{15}{300}=\frac{x}{240}\).

Step2: Solve the proportion

Cross - multiply: \(300x=15\times240\). Then \(300x = 3600\). Divide both sides by \(300\): \(x=\frac{3600}{300}=12\) inches.

Step1: Set up the proportion

Since the original drawing and the projected image are similar, the ratios of their corresponding dimensions (width to height) are equal. Let \(y\) be the width of the projected image. The proportion is \(\frac{7}{4.5}=\frac{y}{27}\).

Step2: Solve the proportion

Cross - multiply: \(4.5y=7\times27\). So \(4.5y = 189\). Divide both sides by \(4.5\): \(y=\frac{189}{4.5}=42\) inches.

Answer:

The length of the model is \(12\) inches.

19)