What are the possible and impossible lengths for a third side of a triangle with two sides being 2 and 4 and the other being 5 and 7(they're two different triangles)

Question

anonymous · Answer

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basically that except for ignore the fact that I made them into right triangles :P

anonymous · Answer

Please help?

mathstudent55 · Answer

The sum of the lenths of any two sides must be greater than the length of the third side.

anonymous · Answer

I tried to do it on my own and got for the first triangle with the length of the 2 sides being 2 and 4 2<x and x<6 and the other triangle with the length of the 2 sides being 5 and 7, 2<x and x<12.... I don't think that's right though and if it is I can't figure out what the impossible length of the the third side would be @mathstudent55

mathstudent55 · Answer

Look at the first triangle: two known sides are 2 and 4. 2 + 4 = 6, so third side must be less than 6, so x < 6. Now look at x and 2. x + 2 > 4 or x > 2. Now look at last group of two sides: x and 4. x + 4 > 2 or x > -2. You have: x < 6 x > 2 x > -2 Since x > 2 is included in x > -2, forget x > -2, so 2 < x < 6 You got the right answer for the first triangle.

mathstudent55 · Answer

You got the second one right also, 2 < x < 12

anonymous · Answer

How would I find out the impossible lengths though? That's what I don't understand @mathstudent55