Question

practice problems
problem 1
an image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor. the actual book is 9 inches wide.
a. what scale is being used for the image?
b. how tall is the actual book?
problem 2
the flag of colombia is a rectangle that is 6 ft long with three horizontal strips.

• the top stripe is 2 ft tall and is yellow.
• the middle stripe is 1 ft tall and is blue.
• the bottom stripe is also 1 ft tall and is red.

a. create a scale drawing of the colombian flag with a scale of 1 cm to 2 ft.
b. create a scale drawing of the colombian flag with a scale of 2 cm to 1 ft.

Explanation:

Problem 1a

Step1: Find the scale

The scale is the ratio of the image - width to the actual width. The image width is 1.5 inches and the actual width is 9 inches.
The scale is $\frac{1.5}{9}=\frac{1}{6}$, which means 1 inch on the image represents 6 inches in actual.

Problem 1b

Step1: Set up a proportion

Let $x$ be the actual height of the book. We know the ratio of image - width to actual width is the same as the ratio of image - height to actual height.
The ratio of image - width to actual width is $\frac{1.5}{9}=\frac{1}{6}$. The image height is 3 inches. So we have the proportion $\frac{3}{x}=\frac{1}{6}$.

Step2: Solve the proportion

Cross - multiply: $x = 3\times6=18$ inches.

Problem 2a

Step1: Convert lengths to centimeters

The length of the flag is 6 ft. With a scale of 1 cm to 2 ft, the length of the flag in the scale - drawing is $\frac{6}{2}=3$ cm.
The top stripe is 2 ft tall. In the scale - drawing, its height is $\frac{2}{2}=1$ cm.
The middle and bottom stripes are 1 ft tall each. In the scale - drawing, their heights are $\frac{1}{2}=0.5$ cm each.
Draw a rectangle 3 cm long with three horizontal stripes: the top stripe 1 cm tall, and the middle and bottom stripes 0.5 cm tall each.

Problem 2b

Step1: Convert lengths to centimeters

The length of the flag is 6 ft. With a scale of 2 cm to 1 ft, the length of the flag in the scale - drawing is $6\times2 = 12$ cm.
The top stripe is 2 ft tall. In the scale - drawing, its height is $2\times2=4$ cm.
The middle and bottom stripes are 1 ft tall each. In the scale - drawing, their heights are $1\times2 = 2$ cm each.
Draw a rectangle 12 cm long with three horizontal stripes: the top stripe 4 cm tall, and the middle and bottom stripes 2 cm tall each.

Answer:

Problem 1a: The scale is 1 inch on the image represents 6 inches in actual.
Problem 1b: The actual height of the book is 18 inches.
Problem 2a: Draw a 3 - cm long rectangle with a 1 - cm tall top stripe and two 0.5 - cm tall bottom stripes.
Problem 2b: Draw a 12 - cm long rectangle with a 4 - cm tall top stripe and two 2 - cm tall bottom stripes.