In this video, let's discuss an interesting property about triangles, the property states that the
sum of any two sides of the triangle will be greater than the third side.
For example, if you are A, B and B, C, that has to be greater than Issie, which is the third side.
Now, we can also think of it in this way.
Imagine is a city and sees a city.
Now, you could travel from a to see in two ways along parts of the triangle.
Right.
You can travel in this way or you can travel from A to B and then from B to C.
Now this part over here will be shorter than traveling from A to B and then from B to C.
Let's try to think a little bit deeper about this.
Over here.
We have a particular triangle right now.
Let's increase AC by increasing its land.
So that would somewhat look like this, right?
So it is now bigger than what is he was over here.
Now, over here we see less than A, B plus B, C, right.
So that's why we are increasing the AC.
That's again in Greece.
Is he the diagram becomes like this.
Now, if you increase more, that's that AC is equal to A, B plus B, C right over here is less than
A, B plus B, C, if you increase it such that AB is equal to A, B plus B, C, it will look like
this.
Right.
So AB plus B.C. is equal to AC, so it does not form a triangle, it's forming a straight line.
So if you have a triangle, definitely the sum of two sides of the triangle will be greater than the
third side.
All right, let's press on let's ride this over here.
Some of two sides of a triangle is greater than the third side.
Now, let's derive one more property on the basis of this property, which we have seen, the difference
of two sides of a triangle will be less then the third side.
Now, let's model the length of the sides of this triangle as A, B and C, the length of the side,
which is opposite angle is taken as smaller three and similarly smaller to B is opposite angle B and
C is opposite angle.
See.
All right.
Now I split this property over here.
We know that A plus B will be greater than C right now.
If I take B to the right hand side, you can see that you get C minus B is less than A, right.
You can write it as it is greater than C minus B, and that's the same as writing A, C minus B is less
than eight.
And that's what we have said over here.
The difference of two sides of a triangle will be less than the third side.
All right, let's take these two properties over here.
Now, see, you are given two sides of a triangle as five and twelve.
So two sides are given.
One side is five and one side is twelve centimetres.
Now, what are all the possible values that the third side can take?
The third side will be greater than twelve minus five and the third side will be less than twelve plus
five.
That is twelve minus five gives you seven to seven less than the third side.
Less than one plus five gives you seventeen.
So if it is given that the third side, for example, is six centimetre, then five, twelve and six
cannot form a triangle, or if it's given that the third side is eighteen centimetre, then five, 12
and 18 cannot form a triangle.
So the third side can only take values in between five and 17.
And remember, it's not including 17 and seven to seven and 17 also can not be the third side.
The values, the integral values that are possible for the third side are eight, nine, ten, eleven.
Up to sixteen.