Let's do this question in the figure below.
Find the sum of the ingredients of Triangle B, Q, R and Triangle P, as are.
All right.
Was the video.
Give it a try and then let's do it together.
All right.
We're back.
Let's do it together.
Over here.
You can see that.
Twenty, fifteen and twenty five.
That is the three sides of triangle P.
Q is form a Pythagoras triplet.
Right.
Why is that so.
The first reason is you can see twenty five squared is equal to twenty squared plus fifteen squared.
Right.
And we have discussed other numbers how to find quickly squares of numbers.
Right.
And there is also a different way in which you can find that this is a Pythagoras triplet.
You can quickly observe that it's related to the Pythagorean Triplette five, four, three.
Now take this Pythagoras Triplette and multiply throughout with five.
So over here, five into five gives you twenty five or in the five gives you twenty and three in the
five gives you fifteen.
So we have already seen that if you take it by the intraplate and multiply it throughout with the number,
you will get another by the intraplate.
All right.
Now having established that twenty fifteen and twenty five former Pythagorean Triplette, therefore
Angle Kupets will be a 90 degree angle, right.
This angle will be a 90 degree angle.
Let's mark the length B are as it's.
All right, now we know that the area of a triangle is equal to half base in height.
Now let's take 15 as the base, then 20, that is space would be the height, right?
If BQ is the base B, as is the height.
So I can right the area of this triangle as half in the 15 or 20.
Or if Q is the base then P R is the height.
Right.
Because this angle has to be 90 degrees over your base is the height because this angle is 90 degrees.
All right.
So if QSA is the base bar is the height.
So they African wilderness often took us into B-R or it's all right.
So let's right that.
So I have half in the 15 and 20, which is the area and we also have half in to us.
That's twenty five in the edge as the area.
Therefore I can equate these two expressions because it's giving us the same area that is the area of
Triangle Kupets.
All right.
Now using this equation, I can find that it is equal to twelve, right?
Often half gets cancelled out.
Over here you have 15.
So you divide it by five, you get three to divide this by fire, you get five and five.
Cut it out from both sides and you're left with four.
So you get it is equal to three in the four, which is equal to twelve to the height over here is twelve
centimeter.
All right.
Now let's take a triangle to our peak.
The Triangle Q, r B is also a right angle triangle.
Right.
Therefore side Q are can be found as root of 15 square minus 12 square.
That gives you nine.
Why is that so.
Because this is the hypotenuse.
Right.
But we know 15 square is equal to Q are squared plus it's square and that is twelve.
Right.
Well squared.
So take this to the other side and you get.
Q What is the square root of 15 square.
Minus 12 square that gives you eighty one and square root of eighty one gives you nine.
So QR is equal to nine, therefore ours would be twenty five minus nine.
Right.
Which is equal to sixteen.
All right.
Now we have established this over here.
Let me right this over here.
Q Are is nine and ours is equal to sixteen.
So let's take this aside.
All right, now let me market over here again.
We have nine and 16 over here and it is equal to 12 already in triangle because you are in this triangle.
You can see that half you are into it will give you the area.
Right, because this angle is 90 degrees.
Therefore, half base in the height is the area that is half you are into it.
And we have seen that the area of a triangle can also be found as the product of the in radius and the
semi perimeter.
So of you are into it is equal to our into S1 where R-1 is the semi inside Iran is the radius of triangle.
You are an S1 is the same perimeter of trying to pick you up.
All right.
So let's substitute the values that gives us nine by two in the 12th is equal to 18 into our.
As one is equal to 18.
Right.
How do you find that 15 plus nine plus 12.
That gives you 36.
Right.
And 36 by two.
Gives you 18.
All right, let's press on.
So from this equation, we can find that R-1 is equal to three.
So the radius of Triangle Park you are is equal to three centimeter.
Similarly, let's take triangle B.
R.
S.
We can ride off into 16 and 12 is equal to our two in the S2 and S2 is equal to forty eight by two,
which gives you twenty four.
Right.
So using this equation you can find that our two is equal to four centimetre and you are asked to find
the sum of the radiuses.
So that would be R one plus R two which is equal to three plus four.
That gives you the answer seven centimetre.
Now in the next video we learn a shortcut to do the same thing much faster.