Question Video: Identifying Whether the Given Side Lengths Are Valid for Constructing a Triangle Mathematics • Second Year of Preparatory School

Video Transcript

Is it possible to form a triangle with side lengths six meters, seven meters, and 18 meters?

To answer this question, we will need to recall the triangle inequality theorem, which tells us that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This means that for any triangle 𝐴𝐵𝐶, 𝐴𝐵 plus 𝐴𝐶 is greater than 𝐵𝐶, 𝐴𝐵 plus 𝐵𝐶 is greater than 𝐴𝐶, and 𝐴𝐶 plus 𝐵𝐶 is greater than 𝐴𝐵.

We are being asked if it’s possible to form a triangle with the lengths of six meters, seven meters, and 18 meters. For this to be the case, these three values must make all three triangle inequalities true. So, we will be checking to see if 18 plus seven is greater than six, if 18 plus six is greater than seven, and if six plus seven is greater than 18.

The first inequality is true because 25 is greater than six. The second inequality is also true because 24 is greater than seven. But when we add the two shorter side lengths, we get 13, which is not greater than the third side length of 18. This means that we cannot form a triangle with side lengths six meters, seven meters, and 18 meters.