\( 3 \mathrm{~cm}, 4 \mathrm{~cm} \) and 7 cm are not the lengths of the triangle. Give the reason.
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To determine if three lengths can form a triangle, we apply the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. Here, we check the combinations: 1. \(3 \, \text{cm} + 4 \, \text{cm} = 7 \, \text{cm}\) (not greater) 2. \(3 \, \text{cm} + 7 \, \text{cm} = 10 \, \text{cm} > 4 \, \text{cm}\) 3. \(4 \, \text{cm} + 7 \, \text{cm} = 11 \, \text{cm} > 3 \, \text{cm}\) The first combination shows that these lengths cannot form a triangle because one side is equal to the sum of the other two, failing the strict inequality required for triangle formation. Thus, a triangle cannot be formed with lengths of \(3 \, \text{cm}\), \(4 \, \text{cm}\), and \(7 \, \text{cm}\).