In this video, let's learn an interesting property for rectangles.
Let me take a rectangle over here.
Now, let me take any point.
Be inside Rectangle.
OK, now over here, I have the vertices before vertices of the rectangle.
Let me join P with the four vertices like this.
Now let me name the former pieces as ABCDE.
Now you will observe that aspect.
This property be A squared plus B C square is equal to Butis squared plus B B squared.
So if you have a point over here, anywhere inside the rectangle, if you join into the vertices and
then the sum of the square of the distance from that point to opposite, what Vertices says will be
equal to be squared plus squared is equal to pretty squared plus B, B square.
Now, let's do an interesting question based on this.
If you know this property, you can do this question very quickly or B is given A three centimeter,
B, B is giving us four centimeter.
B is giving us five centimetre.
And you're asked to find B, C, so as per the property, which we just know, so we can easily find
it to be A squared plus B C squared is equal, pretty squared plus B, B square the three squared plus
B C squared is equal to five squared plus four square Y squared plus four square is twenty five plus
sixteen.
That's forty one APC square is equal to thirty two or pieces equal to the root of 32 which is four to.