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Could a triangle have side lengths of 16ft, 44ft, and 28ft? Explain your answers and thinking.

User Awendt
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1 Answer

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Answer: No, a triangle is NOT possible

Step-by-step explanation

Consider side lengths of: a = 16, b = 28, c = 44

A triangle is only possible if adding any two sides gets a result larger than the third side. This is the triangle inequality theorem

Add the first two sides to get a+b = 16+28 = 44, but this result is NOT larger than the third side c = 44.

Therefore, a+b > c is false and a triangle is NOT possible.

Grab some pieces of string, or slips of paper, to try this out for yourself. Let's say you replace the units "feet" with "inches". You'll find that the 16 inch and 28 inch pieces of string stretch to 44 inches maximum. But it's impossible to form a triangle and instead a straight line forms only.

GeoGebra is another way to confirm the answer.

User Hijarian
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