Question

Hey i need help on these

Determine if the following side lengths will form a triangle using the Triangle Inequality Theorem.

33.7, 62.9, 96.6

A.The three sides do not form a triangle.
B. The three sides do form a triangle.

Answer 1

A. no triangle

Explanation:

You want to know if the Triangle Inequality Theorem allows a triangle from side lengths 33.7, 62.9, and 96.6.

Triangle inequality theorem

The theorem requires for any side lengths a, b, c, this inequality must hold:

a + b > c

Application

Using the given side lengths, we have ...

33.7 +62.9 > 96.6

96.6 > 96.6 . . . . . . . . False

The three sides do not form a triangle.

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Additional comment

These side lengths will join ends to ends to form a "triangle" that looks like a line segment of length 96.6 with a point on it at 33.7 from one end. Most authors do not recognize this figure as a triangle. For those authors who write the theorem as a +b ≥ c, these segments will form a triangle.

You should check your curriculum materials to see whether your Triangle Inequality Theorem uses the > or the ≥ relation.

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