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A metal worker cut an 8-foot length of pipe into three pieces and welded them to form a triangle. Each of the 3 sections measured a whole number of feet in length. How long was each section? Explain your reasoning

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Answer:

2, 3, and 3

Step-by-step explanation:

A rule about triangles is that the sum of any two side lengths must be larger than the remaining side length.  

Since the problems uses whole numbers, we rule out fractions as possible answers.

Lets start with side lengths of

1, 1, and 6....

This doesn't work because 1 + 1 < 6

Now try 1, 2 and 5

This also doesn't work because 1 + 2 < 5

Other possible combinations that don't work for the same reasons are....

1, 3 and 4        (1 + 3 = 4, the two sides must be GREATER that 4)

1, 4, and 3      is the same as 1, 3 and 4

When we try 2, 3 and 3, this works because

2 + 3 > 3,      2 + 3 > 3,     and  3 + 3 > 2

*2 + 3 > 3  us used twice because there are two side length of 2, so one for each

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