Question

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

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check side - length sums

Let \(a = 4\), \(b = 12\), and \(c = 17\). Calculate \(a + b\): \(4+12=16\).

Step3: Compare with the third - side length

Since \(16<17\) (i.e., \(a + b

Answer:

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