Answer:
[tex]\bold{a = \dfrac{24}{7}}[/tex]
Step-by-step explanation:
Kindly refer to the attached for the values labelled to the line XZ.
The point Y is in between XZ.
It can be clearly observed that XZ is made up of sum of two lines XY and YZ.
So, we can write:
XZ = XY + YZ ....... (1)
We are given the values of line segments:
XY = 4a
YZ = 9a and
XZ = 6a+24
To find: Value of variable 'a'.
Solution:
Putting all the values in equation (1):
[tex]6a+24 = 4a + 9a\\\Rightarrow 6a+24=13a\\\Rightarrow 7a=24\\\Rightarrow \bold{a = \dfrac{24}{7}}[/tex]
So, value of variable is
[tex]\bold{a = \dfrac{24}{7}}[/tex]
