Question

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

Answer 1

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:
`3+4\\gtr9` therefore, triangle is not possible

Part B:
`3+6\\gtr9` therefore, triangle is not possible

Part C:
`4+5\\gtr9` therefore, triangle is not possible

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

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

Thus, only Options D and E apply