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.

Answer 1

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

Since 4+12 isnt greater than 17, the triangle doesn't exist

Answer 2

If you have a triangle with sides a, b and c, then:

$a+b>c,\\a+c>b,\\b+c>a.$

In your case let a=4 in, b=12 in annd c=17 in. Check these three inequalities:

1. 4+12=16 is less than 17 - inequality a+b>c doesn't hold.

2. 4+17>12 - inequality a+c>b holds.

3. 12+17>4 - inequality b+c>a holds.

Since only two from three inequalities are true, then the triangle doesn't exist.

Answer: correct choice is D - This triangle does not exist because the sum of 4 and 12 is less than 17.