Question

Given sides 2, 3, 5. Do they form a triangle and what Theorem justifies it.

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10 points
A. YES. Pythagorean Theorem
B. YES. Triangle Inequality Theorem
C. NO. Pythagorean Theorem
D. NO. Triangle Inequality Theorem

Answer 1

The given sides 2, 3, and 5 do not form a triangle according to the Triangle Inequality Theorem. The correct answer is option: C. NO. Pythagorean Theorem.

Step-by-step explanation:

Given sides 2, 3, and 5, we can determine if they form a triangle using the Triangle Inequality Theorem. According to the theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Therefore, to determine if the sides 2, 3, and 5 form a triangle, we add the lengths of all possible pairs of sides:

2 + 3 = 5

2 + 5 = 7

3 + 5 = 8

Since in all cases the sum of the two shorter sides is always less than the longest side (5), the given sides do not form a triangle. Therefore, the correct answer is C. NO. Pythagorean Theorem.