Video: Determining the Possible Lengths of a Triangle’s Sides

Which of the following lists could be the lengths of sides of a triangle? [A] 5, 2, 8 [B] 2, 5, 6 [C] 5, 3, 8

03:29

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.

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