Refer the image attached:
Now, as the question says length of WZ = 28 cm
Length of WX = [tex](a+1)[/tex] cm
Length of YZ = [tex](2a+1)[/tex] cm
Lets say the length of XY = K cm (Refer the image attached)
Now,
Length of WZ = length of WX+ length of XY+ length of YZ
Now, Y is the mid-point of XZ. So the length XY must be equal to the length YZ.
Now, [tex]XY=K= (2a+1)[/tex]
So,
The total length that is the length of WZ should be equal to:
[tex]WX+XY+YZ=(a+1)+(2a+1)+(2a+1)[/tex]
[tex]28= a+1+2a+1+2a+1[/tex]
Solving for 'a', we get:
[tex]28=5a+3[/tex]
[tex]5a=28-3[/tex]
[tex]5a=25[/tex]
[tex]a=\frac{25}{5} =5[/tex]
Now that we have the value of 'a', we can find the length of the mid-section that is XY.
[tex]XY=(2a+1)=2 \times 5+1=10+1=11[/tex]
So, the length of XY is 11 centimeters.
