Question

in a scale drawing of a painting, 1 centimeter represents 6 inches.
answer the following.
(a) in the scale drawing, the length of the painting is 7 centimeters. what is the length of the real painting?
inches
(b) the height of the real painting is 24 inches. what is the height of the painting in the scale drawing?
centimeters

Explanation:

Step1: Analyze part (a)

Given the scale \(1\ cm:6\ in\). For the length of the scale - drawing \(l_{scale}=7\ cm\). Use the proportion \(\frac{l_{scale}}{l_{real}}=\frac{1}{6}\). Then \(l_{real}=l_{scale}\times6\).

Step2: Calculate part (a)

Substitute \(l_{scale} = 7\) into the formula \(l_{real}=7\times6 = 42\) inches.

Step3: Analyze part (b)

Given the scale \(1\ cm:6\ in\). Let the height of the scale - drawing be \(h_{scale}\). We know \(h_{real} = 24\) inches. Using the proportion \(\frac{h_{scale}}{h_{real}}=\frac{1}{6}\), then \(h_{scale}=\frac{h_{real}}{6}\).

Step4: Calculate part (b)

Substitute \(h_{real}=24\) into the formula \(h_{scale}=\frac{24}{6}=4\) centimeters.

Answer:

(a) \(42\) inches
(b) \(4\) centimeters