Question

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

Explanation:

Step1: Recall triangle inequality theorem

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 \(a = 4\), \(b=12\), \(c = 17\)
Check \(a + b\): \(4+12=16\)
Since \(16<17\) (i.e., \(a + b

Answer:

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