Answer: The required value of the variable c is 18 and that of YZ is 72.
Step-by-step explanation: Given that Y is in between X and Z, where
XY= 11, YZ=4c and XZ=83.
We are to find the value of the variable c and YZ.
Since the point Y is in between X and Z, so we must have
[tex]XY+YZ=XZ\\\\\Rightarrow 11+4c=83\\\\\Rightarrow 4c=83-11\\\\\Rightarrow 4c=72\\\\\Rightarrow c=\dfrac{72}{4}\\\\\Rightarrow c=18.[/tex]
And,
[tex]YZ=4c=4\times 18=72.[/tex]
Thus, the required value of the variable c is 18 and that of YZ is 72.
