Question

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Suppose 1 side of a triangle measures 23 inches and another side measures 19 inches. Use the triangle inequality theorem to determine possible side lengths for the third scale. Show work.

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Answer 1

Answer: x > 23 - 19 = 4x > 19 - 23 = -4x < 23 + 19 = 42So the possible side lengths for the third side of the triangle are any value greater than 4 inches or any value less than 42 inches.The inequality is represented as:-4 < x < 42So a possible third side can be any value between -4 and 42 inches

Answer 2

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

So for a triangle with sides of length 23 inches and 19 inches, we can use the triangle inequality theorem to determine the possible side lengths for the third side, x.

The triangle inequality theorem gives us:

x > 23 - 19 = 4

x > 19 - 23 = -4

x < 23 + 19 = 42

So the possible side lengths for the third side of the triangle are any value greater than 4 inches or any value less than 42 inches.

The inequality is represented as:

-4 < x < 42

So a possible third side can be any value between -4 and 42 inches