Question

in a scale model of a television, 1 centimeter represents 8 inches.
answer the following.
(a) the length of the real television is 64 inches. what is the length of the television in the scale model?

centimeters

in the scale model, the height of the television is 9 centimeters. what is the height of the real television?

inches

Explanation:

Step1: Find the length in the scale model for part (a)

Given the scale \(1\space cm:8\space in\). Let \(x\) be the length in the scale model. We use the proportion \(\frac{1\space cm}{8\space in}=\frac{x\space cm}{64\space in}\). Cross - multiply: \(8x = 64\).

Step2: Solve for \(x\) in part (a)

Divide both sides of \(8x = 64\) by \(8\): \(x=\frac{64}{8}=8\).

Step3: Find the real - height for part (b)

Using the scale \(1\space cm:8\space in\). If the height in the model is \(h_m = 9\space cm\), and let the real height be \(h_r\). Then \(\frac{1\space cm}{8\space in}=\frac{9\space cm}{h_r}\). Cross - multiply: \(h_r=9\times8\).

Step4: Calculate \(h_r\) in part (b)

\(h_r = 72\).

Answer:

(a) \(8\) centimeters
(b) \(72\) inches