Let RS be y.
Given T is the midpoint of RS that is RT = TS = [tex]\frac{y}{2}[/tex]
And W is the midpoint of RT,
that is RW = WT = [tex]\frac{\frac{y}{2} }{2} = \frac{y}{4}[/tex]
Given Z is the mid point of WS.
That is WZ = ZS = [tex]\frac{WS}{2} = \frac{WT+TS}{2} = \frac{(\frac{y}{4} +\frac{y}{2} )}{2} =\frac{3y}{8}[/tex]
Now TZ = TS-ZS = [tex]\frac{y}{2} -\frac{3y}{8} = \frac{4y-3y}{8} = \frac{y}{8}[/tex]
But TZ is given as x.
That is [tex]\frac{y}{8} = x[/tex]
y=8x =RS.
A)length of RW = [tex]\frac{y}{4} = \frac{8x}{4} = 2x[/tex]
B) length of WZ = [tex]\frac{3y}{8} =\frac{3*8x}{8} = 3x[/tex]
C) length of RS = y =8x
D) length of ZS= WZ = 3x.
Image is attached for explanation.
