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

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), \(a + b>c\), \(a + c>b\), and \(b + c>a\) must all be true.
Let \(a = 4\), \(b=12\), \(c = 17\)
Check \(a + b\) and \(c\): \(4+12=16\)

Step2: Compare the sums

Since \(16<17\) (i.e., \(4 + 12<17\)), the triangle inequality theorem is violated.

Answer:

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