Asked by martin
Which are side lengths of quadrilateral PQRS? Check all that apply.
4 units
5 units
6 units
units
4 units
All Answers 1
Answered by
GPT-5 mini
AI
I don’t have enough information to pick among the given choices — the options you posted look incomplete/garbled (there’s a blank entry and “4 units” appears twice). Could you repost the full list or the diagram for quadrilateral PQRS?
If you meant to ask in general which sets of four numbers can be the side lengths of a (simple or convex) quadrilateral, use this test:
- A set of four positive numbers a, b, c, d can be the side lengths of a simple (nondegenerate) quadrilateral iff the longest number is strictly less than the sum of the other three. (If it equals the sum of the other three you get a degenerate “quadrilateral” with all vertices collinear.)
Example checks:
- {4,5,6,7}: 7 < 4+5+6 = 15 → possible.
- {4,5,6,15}: 15 ≥ 4+5+6 = 15 → not possible (degenerate).
- {4,4,5,6}: 6 < 4+4+5 = 13 → possible.
If you provide the exact choices (and any diagram), I’ll apply the test and mark which ones work.
If you meant to ask in general which sets of four numbers can be the side lengths of a (simple or convex) quadrilateral, use this test:
- A set of four positive numbers a, b, c, d can be the side lengths of a simple (nondegenerate) quadrilateral iff the longest number is strictly less than the sum of the other three. (If it equals the sum of the other three you get a degenerate “quadrilateral” with all vertices collinear.)
Example checks:
- {4,5,6,7}: 7 < 4+5+6 = 15 → possible.
- {4,5,6,15}: 15 ≥ 4+5+6 = 15 → not possible (degenerate).
- {4,4,5,6}: 6 < 4+4+5 = 13 → possible.
If you provide the exact choices (and any diagram), I’ll apply the test and mark which ones work.
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