### Video Transcript

Which of the following lists could
be the length of sides of a triangle, A) five, two, eight; B) two, five, six; or C)
five, three, eight?

To enable us to solve this problem,
we actually have this relationship. And this relationship is that the
sum of the lengths of any two sides of a triangle is greater than the length of the
third side. So we can actually use this
relationship to help us decide which of our lists can create a triangle.

And what we’re gonna do is actually
check each of our lists in turn. And to do this, we’re actually
gonna be comparing the sum of each pair of sides or values that we’re given. So I’m gonna begin with A. So we have five, two, eight, and
I’ve labelled these 𝑎, 𝑏, and 𝑐. So we’re gonna start with 𝑎 plus
𝑏 is greater than 𝑐 because, as it says, the sum of the lengths of any two sides
of a triangle is greater than the length of third side.

So this gives us five plus two is
greater than eight. So okay, actually we get seven is
greater than eight. Well this isn’t true, so we can say
false. So therefore, we know already that
A cannot be the length of sides of a triangle. Because if two of the sides added
together isn’t greater than the length of the third side, then we know that they
cannot be the sides of a triangle.

This time we’re gonna have a look
at B. So we’ve got two, five, six. So again, we look at 𝑎 plus 𝑏 is
greater than 𝑐. So we get two plus five is greater
than six. So seven is greater than six. This is true. So great! We’re now gonna go on and compare
another pair of values. So this time I’m gonna do 𝑎 plus
𝑐 is greater than 𝑏, which gives us two plus six is greater than five. So yes! Great! This is another one that’s correct
because eight is greater than five.

So we’ve had two comparisons, and
they’ve both been true. So now what we need to do is
compare the final pair of values. So this time we have 𝑏 plus 𝑐 is
greater than 𝑎, which gives us five plus six is greater than two. So we get 11 is greater than two
which, again, is correct. So as we have the sum of the
lengths of any two sides of our triangle being greater than the length of the third
side, we can say that therefore list B can be the lengths of sides of a
triangle.

Okay, now let’s move on to list
C. So we have five, three, eight. And again, I’ve labelled them 𝑎,
𝑏, and 𝑐. And as previously, we’re gonna
start with 𝑎 plus 𝑏 is greater than 𝑐. So we get five plus three is
greater than eight. Well this is in fact false because
eight is not greater than eight. Eight is equal to eight. So therefore, we can say that list
C cannot be the lengths of sides of a triangle.

And therefore, we can say, in
answer to our question, the only list that could be the lengths of sides of a
triangle is list B, which is two, five, six.