Question

Find the value of the variable. if Y is between X and Z.

segment XY = 4a and segment YZ = 9a and segment XZ = 6a+24

Answer 1

`\bold{a = (24)/(7)}`

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):

`6a+24 = 4a + 9a\\\Rightarrow 6a+24=13a\\\Rightarrow 7a=24\\\Rightarrow \bold{a = (24)/(7)}`

So, value of variable is

`\bold{a = (24)/(7)}`