Question

in a scale model of a table, 1 centimeter represents 8 inches. scale 1 cm : 8 in answer the following. (a) the height of the real table is 48 inches. what is the height of the table in the scale model? centimeters (b) in the scale model, the length of the table is 9 centimeters. what is the length of the real table? inches

Explanation:

Part (a)

Step1: Identify the scale ratio

The scale is \(1\) cm : \(8\) in, meaning \(1\) cm in model = \(8\) in real.

Step2: Set up proportion for height

Let \(x\) be the model height (in cm). We have \(\frac{1}{8}=\frac{x}{48}\).

Step3: Solve for \(x\)

Cross - multiply: \(8x = 48\times1\), then \(x=\frac{48}{8}=6\).

Part (b)

Step1: Use the scale ratio

Scale is \(1\) cm : \(8\) in, so model length (in cm) times \(8\) gives real length (in in).

Step2: Calculate real length

Model length is \(9\) cm, so real length \(=9\times8 = 72\) inches.

Part (a) Answer: \(6\)

Part (b) Answer: \(72\)

Answer:

Step1: Use the scale ratio

Scale is \(1\) cm : \(8\) in, so model length (in cm) times \(8\) gives real length (in in).

Step2: Calculate real length

Model length is \(9\) cm, so real length \(=9\times8 = 72\) inches.

Part (a) Answer: \(6\)

Part (b) Answer: \(72\)