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Magazine scale: 1 inch = 2 feet. Yosef's scale: 2 inches = 3 feet. Triangle A B C. Side A is 3 inches, side B is 7 inches, and side C is 11 inches. Yosef saw a garden in a magazine that has a scale of 1 inch to 2 feet. He has less space, so his scale will be 2 to 3. Check all that apply. Length A in the magazine’s garden is 6 feet. Length A in Yosef’s garden is 4.5 feet. Length B in the magazine’s garden is 14 feet. Length B in Yosef’s garden is 10.5 feet. Length C in the magazine’s garden is 13 feet. Length C in Yosef’s garden is 16.5 feet.

Question

Magazine scale: 1 inch = 2 feet. Yosef's scale: 2 inches = 3 feet. Triangle A B C. Side A is 3 inches, side B is 7 inches, and side C is 11 inches. Yosef saw a garden in a magazine that has a scale of 1 inch to 2 feet. He has less space, so his scale will be 2 to 3. Check all that apply.

Length A in the magazine’s garden is 6 feet. Length A in Yosef’s garden is 4.5 feet. Length B in the magazine’s garden is 14 feet. Length B in Yosef’s garden is 10.5 feet. Length C in the magazine’s garden is 13 feet. Length C in Yosef’s garden is 16.5 feet.

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Solution 1

The magazine scale is 1 inch = 2 feet. Therefore, for triangle ABC:

  • Length A in the magazine’s garden is 3 inches * 2 feet/inch = 6 feet. This statement is correct.
  • Length B in the magazine’s garden is 7 inches * 2 feet/inch = 14 feet. This statement is correct.
  • Length C in the magazine’s garden is 11 inches * 2 feet/inch = 22 feet. The statement that length C in the magazine’s garden is 13 feet is incorrect.

Yosef's scale is 2 inches = 3 feet. Therefore, for triangle ABC:

  • Length A in Yosef’s garden is 3 inches * (3 feet/2 inches) = 4.5 feet. This statement is correct.
  • Length B in Yosef’s garden is 7 inches * (3 feet/2 inches) = 10.5 feet. This statement is correct.
  • Length C in Yosef’s garden is 11 inches * (3 feet/2 inches) = 16.5 feet. This statement is correct.

This problem has been solved

Solution 2

The scales given are as follows:

  • Magazine scale: 1 inch = 2 feet
  • Yosef's scale: 2 inches = 3 feet

We can use these scales to calculate the lengths of the sides of the triangle in the magazine's garden and in Yosef's garden.

  1. Length A in the magazine’s garden is 3 inches * 2 feet/inch = 6 feet. This statement is correct.
  2. Length A in Yosef’s garden is 3 inches * 3 feet/2 inches = 4.5 feet. This statement is correct.
  3. Length B in the magazine’s garden is 7 inches * 2 feet/inch = 14 feet. This statement is correct.
  4. Length B in Yosef’s garden is 7 inches * 3 feet/2 inches = 10.5 feet. This statement is correct.
  5. Length C in the magazine’s garden is 11 inches * 2 feet/inch = 22 feet. The statement that length C in the magazine's garden is 13 feet is incorrect.
  6. Length C in Yosef’s garden is 11 inches * 3 feet/2 inches = 16.5 feet. This statement is correct.

So, the correct statements are:

  • Length A in the magazine’s garden is 6 feet.
  • Length A in Yosef’s garden is 4.5 feet.
  • Length B in the magazine’s garden is 14 feet.
  • Length B in Yosef’s garden is 10.5 feet.
  • Length C in Yosef’s garden is 16.5 feet.

This problem has been solved

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