Question

in a scale drawing of a painting, 1 centimeter represents 7 inches.
answer the following.
(a) in the scale drawing, the length of the painting is 9 centimeters. what is the length of the real painting?
inches
(b) the height of the real painting is 28 inches. what is the height of the painting in the scale drawing?
centimeters

Explanation:

Step1: Solve part (a)

Given the scale \(1\ cm:7\ in\). If the length in the scale drawing is \(x = 9\ cm\), then using the proportion \(\frac{\text{Scale length}}{\text{Real length}}=\frac{1}{7}\). Let \(y\) be the real - length. We have \(y=9\times7\).

Step2: Calculate the value of \(y\)

\(y = 9\times7=63\) inches.

Step3: Solve part (b)

Let \(h\) be the height in the scale drawing. Given the real height \(H = 28\) inches. Using the proportion \(\frac{h}{H}=\frac{1}{7}\). So \(h=\frac{28}{7}\).

Step4: Calculate the value of \(h\)

\(h=\frac{28}{7}=4\) centimeters.

Answer:

(a) \(63\) inches
(b) \(4\) centimeters