Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using the

scale 1 inch:2 feet.

(a) What is the length of the garden in her model? Show your work, including your proportion

(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model

drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?

(a) 3 inches

(b) Her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches because the dimensions are not proportional to the scale.

Explanation:

(a) What is the length of the garden in her model? Show your work, including your proportion

1. Scale:

model length / real length = 1 inch / 2 feet

2. Proportion:

Naming x the model length:

1 inch / 2 feet = x / 6 feet

Cross multiply:

1 inch * 6 feet = 2 feet * x

Divide both sides by x:

x = 1 inch * 6 feet / 2 feet = 3 inch.

Answer: 3 inches

(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?

Both the width and the length must use the same scale, thus the corresponding sides of the scale model and the drawing must be proportional.

In the model the ratio of the length to the width is 3 inch / 5 inch

In the paper the ratio of the length to the width is 8.5 inch / 7 inch

Hence, you can see that in the model the length (mumerator of the fraction) is less than the width (denominator) while in the paper it is the opposite. Bieng the two ratios different, they are not proportional, and you conclude that her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches.