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Select all the sets of side lengths that will make a triangular shelf fit in a 90° corner of a room

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Select all the sets of side lengths that will make a triangular shelf fit in a 90° corner of a room.
6 cm, 8 cm, 10 cm
2 cm, 3 cm, 4 cm
5 cm, 6 cm, 9 cm
3 cm, 4 cm, 5 cm
7 cm, 9 cm, 11 cm




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    1 Answer

    1. Quizzma Team

      To determine which sets of side lengths can form a triangle that fits in a 90° corner, we need to apply the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

      Let’s evaluate each set of side lengths:

      1. 6 cm, 8 cm, 10 cm:

      – 6 + 8 > 10 (True)

      – 6 + 10 > 8 (True)

      – 8 + 10 > 6 (True)

      – This set is valid.

      2. 2 cm, 3 cm, 4 cm:

      – 2 + 3 > 4 (False)

      – This set is not valid.

      3. 5 cm, 6 cm, 9 cm:

      – 5 + 6 > 9 (False)

      – This set is not valid.

      4. 3 cm, 4 cm, 5 cm:

      – 3 + 4 > 5 (True)

      – 3 + 5 > 4 (True)

      – 4 + 5 > 3 (True)

      – This set is valid.

      5. 7 cm, 9 cm, 11 cm:

      – 7 + 9 > 11 (True)

      – 7

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