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Write the inequality for the range of the length of the third side of a triangle given the following two side lengths: 10 and 16.

User Karloss
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Final answer:

The inequality for the range of the length of the third side of a triangle, given two side lengths of 10 and 16, is c < 26.

Step-by-step explanation:

To find an inequality for the range of the length of the third side of a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's denote the two given side lengths as a = 10 and b = 16. The inequality for the range of the length of the third side, c, would be:

a + b > c

Substituting the given values, we have:

10 + 16 > c

26 > c

Therefore, the range for the length of the third side of the triangle is c < 26, meaning the third side must be less than 26 units.

User Nace
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