Proportional relationships are another important part of geometric problem solving.

A woodblock painting has dimensions of 60 centimeters by 79.5 centimeters. In order to fit on a flyer advertising the opening of a new art show, the image must be reduced by a scale factor of 1 over 25 1 25 . What will be the final dimensions of the image on the flyer?

Image of the sun over a Japanese temple
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Drag the tiles representing the numbers to their appropriate place in the proportion below.

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Hint

Multiply the original dimensions by the scale factor indicated in the problem. You may need to convert rational numbers from one form to another (e.g., fractions to decimals). Close Pop Up

Measuring Problem

For summer vacation, Jennifer and her family drove from their home in Inlandton to Beachville. Their car can drive 20 miles on one gallon of gasoline. Use the ruler to measure the distance that they drove to the
nearest 1 over 4 1 4 - inch, and then calculate the number of gallons of gasoline their car will use at this rate to drive from Inlandton to Beachville.

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Step 1: Read, understand, and interpret the problem.

  • What information is presented?

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    Check Your Answer

    The locations of Inlandton and Beachville are shown.
    We know that the car will drive 20 miles on 1 gallon of gasoline.
    We know that 1 inch on the map represents 80 miles on the road. Close Pop Up
  • What is the problem asking me to find?

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    Check Your Answer

    We need to find the number of gallons of gasoline used to drive from Inlandton to Beachville. Close Pop Up
  • What information may be extra information that I do not need?

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    Check Your Answer

    The location of Port Angelina is extra information. Close Pop Up
Step 2: Make a plan.

  • Draw a picture.
Step 3: Implement your plan.

  • What formulas do I need?

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    Check Your Answer

    We will need to set up a proportion. Close Pop Up
  • What information can I interpret from the diagram, table, or other given information?

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    Check Your Answer

    The road between Inlandton and Beachville is a straight line that measures 4 inches in length. Close Pop Up
  • Solve the problem.

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    Check Your Answer

    Answer: 16 gallons
    Close Pop Up
Step 4: Evaluate your answer.

  • Does my answer make sense?

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    Check Your Answer

    Yes.
    Jennifer and her family drove a total of 4 inches on the map. According to the scale, 1 inch equals 80 miles, so for each inch they drove on the map, the car consumed 4 gallons of gasoline. 4 inches × 4 gallons per inch = 16 gallons. Close Pop Up
  • Did I answer the question that was asked?

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    Check Your Answer

    Yes. I was asked to determine number of gallons, not the number of miles. Close Pop Up
  • Are my units correct?

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    Check Your Answer

    Yes. Our answer is in gallons, which matches the question being asked.Close Pop Up

Practice #1

A blueprint for a rectangular tool shed has dimensions shown in the diagram below.

blueprint showing that the length is 4.5 centimeters and the width is 3.5 centimeters, and a scale of 1 centimeter = 2 feet

Todd is using this blueprint to build a tool shed, and he wants to surround the base of the tool shed with landscaping timbers as a border. How many feet of landscaping timbers will Todd need?


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Hint

You need to use the scale factor to determine the actual dimensions of the tool shed then determine the perimeter of the tool shed.Close Pop Up
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Check Your Answer

First, determine the actual dimensions of the tool shed.

Next, determine the perimeter of the tool shed.
Perimeter = 7 feet + 9 feet + 7 feet + 9 feet = 32 feet Close Pop Up

Practice #2

A scale model of a locomotive is shown. Use the ruler to measure the dimensions of the model to the
nearest 1 over 4 1 4 - inch, and then calculate the actual dimensions of the locomotive.

Interactive exercise. Assistance may be required.
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Hint

Use your measurements to set up and solve a proportion. Close Pop Up
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Check Your Answer

11 1 over 4 1 4 feet by 10 feet
First, measure the scale model:

Next, determine the actual dimensions of the locomotive.
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