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.
