Let's do this question, are I see is a robust find, X, Y, Z, and find the perimeter of the rhombus.
All right.
Was the video.
Give it a try and then let's do it together.
All right.
We're back.
I hope you've given it a try.
Now, over here, you can see that angle EOC will be equal to 90 degree, right?
Because in a rhombus, the diagonals bisect each other at ninety degrees.
All right.
Now you can see that X Square is equal to five squared plus 12 square.
Right, because triangle E, C or is the right angle triangle and X is the hypotenuse.
So as Pythagoras theorem is square is equal to five squared plus twelve squared, that's twenty five
plus one forty four which is equal to one sixty nine.
Therefore X equals root of one sixty nine, that's thirteen.
So we have found the side of the rhombus.
Now Z over here also will be equal to thirteen because all the sides of rhombus are equal.
And what would be the perimeter of the rhombus.
That would be four times Z which is four in the thirteen or fifty two.
All right.
Now, so we have found now we need to find X and Y, OK?
So we know that the diagonals of a rhombus bisect each other.
Why is that so?
Because a rhombus is a parallelogram.
Right?
And in a program, the diagonals bisect each other.
All right.
So I can say that five is equal to plus two and twelve is equal to Y plus X..
Let's write that down.
Five is equal to X plus two and twelve is equal to Y plus X from this five is equal to X plus two.
We can find that X is equal to three and substitute that over here and you get Y is equal to nine to
begin, X is equal to three, Y is equal to nine and Z is equal to thirteen.
And that is your answer.