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Find the range for the measure of the third side of a triangle when the measures of the other two sides are 2 km and 42 km.

Question

Find the range for the measure of the third side of a triangle when the measures of the other two sides are 2 km and 42 km.

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Solution

In a triangle, the length of any side must be less than the sum of the lengths of the other two sides, and more than the absolute difference of the lengths of the other two sides. This is known as the triangle inequality theorem.

  1. First, find the sum of the lengths of the two given sides: 2 km + 42 km = 44 km. The length of the third side must be less than this sum.

  2. Next, find the absolute difference of the lengths of the two given sides: |2 km - 42 km| = 40 km. The length of the third side must be more than this difference.

Therefore, the range for the measure of the third side of the triangle is between 40 km and 44 km.

This problem has been solved

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