7
QuizMultiple Choice

Triangle Inequalities

Question 7 • Q5 Geometry New 2022

Is it possible to construct a triangle with side lengths of 15 inches, 17 inches, and 32 inches? Why or why not?

Answer
A
No, because 15 + 17 > 32.
B
No, because the sum of the lengths of any two sides is not greater than the length of the third side.
C
Yes, because 15 + 17 = 32.
D
Yes, because 15 + 17 < 32.

Explanation

A triangle can be constructed only if the sum of the lengths of any two sides is greater than the third side. Here, 15 + 17 = 32, which is not greater than 32, so these lengths cannot form a triangle. Choice B correctly states the reason; choice A is incorrect because 15 + 17 is equal to 32, not greater.

AI-written and checked against the verified answer.

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