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: Check triangle inequality

Triangle inequality: sum of any two sides > third side.

Step2: Calculate sums of sides

$4 + 12 = 16$, which is less than 17.

Step3: Determine existence

Since $4+12 < 17$, the triangle does not exist.

Answer:

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