Florian and michelle are trying to construct a triangle. florian says the side lengths could be 6, 8, and 10, and the angles of the triangle should have measures of 37°, 53°, and 90°. michelle says the side lengths could be 7, 7, and 14, and the angles should have measures of 35°, 65°, and 80°. which of the friends has the correct measurement for the triangle? how do you know? florian has the correct side lengths because they are all even numbers. florian has the correct side lengths because the measurements fit the triangle inequality rule. michelle has the correct side lengths because they are not all even numbers. michelle has the correct side lengths because their measurements fit the triangle inequality rule.

Question

Mathematics

Deshawn Lloyd

6 February, 08:04

Florian and michelle are trying to construct a triangle. florian says the side lengths could be 6, 8, and 10, and the angles of the triangle should have measures of 37°, 53°, and 90°. michelle says the side lengths could be 7, 7, and 14, and the angles should have measures of 35°, 65°, and 80°. which of the friends has the correct measurement for the triangle? how do you know? florian has the correct side lengths because they are all even numbers. florian has the correct side lengths because the measurements fit the triangle inequality rule. michelle has the correct side lengths because they are not all even numbers. michelle has the correct side lengths because their measurements fit the triangle inequality rule.

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Answers (1)

Know the Answer?

Aliza Stout · Answer 1

The correct answer is:

Florian has the correct side lengths because the measurements fit the triangle inequality rule.

Explanation:

The triangle inequality rule states that the sum of any two sides of a triangle must be greater than the third side.

For Florian's measurements, we have:

6+8 > 10

6+10 > 8

8+10 > 6

These measurements work.

Conversely, Michelle's measurements:

7+7 = 14.

This is not greater than, so this does not work.