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\( 3 \mathrm{~cm}, 4 \mathrm{~cm} \) and 7 cm are not the lengths of the triangle. Give the reason.

Ask by Powers Blake. in Pakistan
Mar 10,2025

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Answer

The lengths 3 cm, 4 cm, and 7 cm cannot form a triangle because the sum of the two smaller lengths (3 cm + 4 cm = 7 cm) is not greater than the largest length (7 cm).

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Bonus Knowledge

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 \(7 \, \text{cm}\).

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