Question

in a scale drawing of a painting, 1 centimeter represents 4 inches. answer the following. (a) the height of the real painting is 40 in. what is the height of the painting in the scale drawing? (b) in the scale drawing, the length of the painting is 8 centimeters. what is the length of the real painting?

Explanation:

Part (a)

Step1: Identify the scale

The scale is given as \(1\) cm represents \(4\) inches. Let the length of the painting in the scale drawing be \(x\) cm and the real length be \(40\) inches. We can set up a proportion using the scale: \(\frac{1\ \text{cm}}{4\ \text{inches}}=\frac{x\ \text{cm}}{40\ \text{inches}}\)

Step2: Solve the proportion

Cross - multiply the proportion: \(4\times x = 1\times40\)
Then, solve for \(x\): \(x=\frac{40}{4}=10\)

Step1: Identify the scale and drawing length

The scale is \(1\) cm : \(4\) inches and the length of the painting in the scale drawing is \(8\) inches? Wait, no, the length in the drawing is \(8\) cm (assuming the unit in the drawing is cm as per the scale). We use the scale to find the real length. If \(1\) cm represents \(4\) inches, and the drawing length \(l = 8\) cm.

Step2: Calculate the real length

The real length \(L\) is given by the formula \(L=\text{drawing length}\times\text{scale factor}\). The scale factor is \(4\) inches per cm. So \(L = 8\times4=32\) inches.

Answer:

The length of the painting in the scale drawing is \(10\) centimeters.

Part (b)