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.

## Step 1<br />The problem involves determining the validity of a triangle given its side lengths. The side lengths are 4 inches, 12 inches, and 17 inches. We need to apply the triangle inequality theorem to solve this problem.<br /><br />### **The Triangle Inequality Theorem**: <br />The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.<br /><br />## Step 2<br />We need to check if the given side lengths satisfy the triangle inequality theorem. We can do this by adding the lengths of any two sides and comparing the sum with the length of the third side.<br /><br />## Step 3<br />Let's add the lengths of the two shorter sides, which are 4 inches and 12 inches. The sum is 16 inches.<br /><br />## Step 4<br />We compare this sum with the length of the longest side, which is 17 inches. Since 16 inches is less than 17 inches, the sum of the two shorter sides is not greater than the length of the longest side.