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Which group of side lengths are possible sides of a triangle? *2 x 5 x 104x4x714 x 11 x 68 x 8 x 82 x 20 x 24A triana

User Aditya Kakirde
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1 Answer

15 votes
15 votes

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

• For the first option, the first two sides sum up to 7 (2 + 5) 7 is less than 10, then these cannot be the lengths of the sides of a triangle.

• When you sum up any two sides of the second option, you get a number that is greater than the third side, like this:

4 + 4 > 7, 8 > 7

4 + 7 > 4, 11 > 4

Then, the second option 4×4×7 is a possible group of lengths for a triangle

• For the third option 14×11×6 its also possible to prove that these lengths can represent a triangle, like this:

14 + 11 > 16, 25 > 16

11 + 6 > 14, 17 > 14

14 + 6 > 11, 20 > 11

• It is well known that there are triangles whose three sides have the same lengths (equilateral triangle) then there is no need to prove it, these lengths are possible for a triangle.

• These lengths can't be possible for a triangle, since 22 (2+20) is not greater than 24 (the third side).

Then only the second (4×4×7), the third (14×11×16) and the fourth (8×8×8) options are possible sides of a triangle.

User Nick Meldrum
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