SOLUTION: If DE = 37 cm and EF = 14 cm, then what are the possible lengths for DF so that line DE, line EF, and line DF can form a triangle? Explain your reasoning.

Question 926073: If DE = 37 cm and EF = 14 cm, then what are the possible lengths for DF so that line DE, line EF, and line DF can form a triangle? Explain your reasoning.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
x = length of missing side

it turns out that if you have a triangle with sides a,b,c with c being the missing side, then c is going to make the following true:

a-b < c < a+b

Note: this implies that a >= b

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in this case, x = c, a = 37 and b = 14, so...

a-b < c < a+b

37-14 < x < 37+14

23 < x < 51

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Final Answer:

The possible lengths for DF are any length between 23 and 51. You do NOT include 23 and you do NOT include 51.

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