Question

in a scale drawing of a house, 1 inch represents 6 feet. answer the following. (a) in the scale drawing, the height of the house is 5 inches. what is the height of the real house? feet (b) the length of the real house is 42 feet. what is the length of the house in the scale drawing? inches

Explanation:

Step1: Analyze part (a)

Given the scale \(1\) inch \(:6\) feet. If the scale - drawing height is \(5\) inches, we use the proportion. Let \(x\) be the real - height. The proportion is \(\frac{1}{6}=\frac{5}{x}\). Cross - multiply: \(x = 5\times6\).

Step2: Calculate part (a)

\(x=5\times6 = 30\) feet.

Step3: Analyze part (b)

Let \(y\) be the scale - drawing length. Using the proportion \(\frac{1}{6}=\frac{y}{42}\). Cross - multiply: \(6y=42\).

Step4: Calculate part (b)

Solve for \(y\): \(y=\frac{42}{6}=7\) inches.

Answer:

(a) \(30\) feet
(b) \(7\) inches