Question

Determine if it is possible to form a triangle using the set of segments with the given measurements.

4.5 in., 5.6 in, 10 in.

a) No, adding all three sides does not add up to the correct measurements.

b) No, because two sides add up to less than the third one.

c) No, because two sides add up to more than the third one.

d) Yes, because two sides add up to less than the third one.

e) Yes, because two sides add up to more than the third one.

Answer 1

• e) Yes, because two sides add up to more than the third one.

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Apply the Triangle Inequality Theorem.

It states that:

• For a triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side.

We'll take the sum of two shortest sides and compare with the longest:

• 4.5 + 5.6 = 10.1 > 10

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).