analyzing triangle side lengths\ngemma wants to draw a triangle with side lengths of 4 inches, 12 inches…

analyzing triangle side lengths\ngemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. which statement is true?\nthis triangle exists because the sum of any two side lengths is greater than the length of the third side.\nthis triangle exists because the sum of 4 and 12 is less than 17.\nthis triangle does not exist because the sum of any two side lengths is greater than the length of the third side.\nthis triangle does not exist because the sum of 4 and 12 is less than 17.

analyzing triangle side lengths\ngemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. which statement is true?\nthis triangle exists because the sum of any two side lengths is greater than the length of the third side.\nthis triangle exists because the sum of 4 and 12 is less than 17.\nthis triangle does not exist because the sum of any two side lengths is greater than the length of the third side.\nthis triangle does not exist because the sum of 4 and 12 is less than 17.

Answer

Explanation:

Step1: Recall triangle side - length rule

For a triangle with side lengths (a), (b), and (c), the following must hold: (a + b>c), (a + c>b), and (b + c>a).

Step2: Check the given side lengths

Let (a = 4), (b = 12), and (c = 17). Check (a + b): (4+12=16). Since (16<17) (i.e., (a + b<c)), the triangle side - length rule is violated.

Answer:

This triangle does not exist because the sum of 4 and 12 is less than 17.