The value of x and YZ is x = 5 units and YZ = 5 units
Given: XY = 4x, YZ = x, XZ = 25 and Y is between X and Z.
This question is based on segment bisector theorem.
What is segment bisector theorem?
The segment bisector theorem states that for a line segment XZ whose length is unknown and if there is a point Y within the line XZ and the length of Y from X and Y from Z is known, that is XY and YZ are of known lengths then we can give the length of line XZ as:
XZ = XY + YZ
How to use segment bisector theorem?
Let's say a line segment XZ is given and the length is unknown.
There is a point Y within the line segment XY where value of XY and YZ are known. Say , XY = a and YZ = b.
So we kind find the length of XZ by direct application of the theorem that is XZ = XY + YZ
Therefore XZ = a + b.
The length of XZ is known.
Similarly if the length of XZ was known and Y was a point within the line segment XZ. The length of only XY was known, We could have find the length of YZ by YZ = XZ - XY and so on.
Now, let's solve the problem.
As Y is between is X and Z, so Y is a point on the line segment XZ and Y is dividing the line segment into two parts namely XY and YZ.
so, XY + YZ = XZ
4x + x = 25
5x = 25
x = 25 / 5
x = 5
YZ = x = 5
Hence x = 5 units and YZ = 5 units
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