which sets of side lengths could form a triangle? Choose all that apply A. 3 centimeters,4 centimeters,9 centimeters B. 3 centimeters, 6 centimeters,9 centimeters C. 4 centimeters, 5 centimeters, 9 centimeters D. 4 centimeters, 6 centimeters, 9 centimeters E. 5 Centimeters, 5 centimeters, 9 centimeters

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11-03-2018
Mathematics

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which sets of side lengths could form a triangle? Choose all that apply A. 3 centimeters,4 centimeters,9 centimeters B. 3 centimeters, 6 centimeters,9 centimeters C. 4 centimeters, 5 centimeters, 9 centimeters D. 4 centimeters, 6 centimeters, 9 centimeters E. 5 Centimeters, 5 centimeters, 9 centimeters

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Vespertilio Vespertilio · Answer 1 · 2018-08-21T09:40:01+02:00

To solve this question we will have to make use of the triangle inequality which states that "the sum of the lengths of any two sides of a triangle must be greater than the length of the third side".

Let us now use this inequality to check Part A to Part E.

Part A: [tex] 3+4\ngtr9 [/tex] therefore, triangle is not possible

Part B: [tex] 3+6\ngtr9 [/tex] therefore, triangle is not possible

Part C: [tex] 4+5\ngtr9 [/tex] therefore, triangle is not possible

Part D: [tex] 4+6>9, 4+9>6, 6+9>4 [/tex] As all the three sides adhere to the triangle inequality, a triangle is possible with these dimensions.

Part E: [tex] 5+5>9, 5+9>5, 9+5>5 [/tex] As all the three sides adhere to the triangle inequality, a triangle is possible with these dimensions.

Thus, only Options D and E apply