Question

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

Explanation:

Step1: Set up proportion for part (a)

Let $x$ be the height in scale - drawing. We have the proportion $\frac{1\ cm}{6\ in}=\frac{x}{24\ in}$.

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

Cross - multiply: $6x = 24\times1$, so $x=\frac{24}{6}=4$ cm.

Step3: Set up proportion for part (b)

Let $y$ be the length of the real painting. The proportion is $\frac{1\ cm}{6\ in}=\frac{7\ cm}{y}$.

Step4: Solve for $y$ in part (b)

Cross - multiply: $1\times y=6\times7$, so $y = 42$ inches.

Answer:

(a) 4
(b) 42