Help! I don't know how to do this question

[Yunie]

A line XY is produced to a point Z such that (YZ - XY)^2 = XZ = XY.

Given that YZ = 9cm, find

(a) the length of XY,

(b) the ratio YZ : XZ


Please explain your workings. Thanks a lot. :-)

[krtxmrtz]

A line XY is produced to a point Z such that (YZ - XY)^2 = XZ = XY.

Given that YZ = 9cm, find

(a) the length of XY,

(b) the ratio YZ : XZ


Please explain your workings. Thanks a lot. :-)

I'm not sure I understand this correctly: do X, Y and Z represent points and are XY, YZ and ZX the segments connecting them?

[Yunie]

I think so...I also don't really understand the question...

[krtxmrtz]

Let me preplace the notation by defining:

a = line from X to Y
b = line from Y to Z
c = line from Z to X

Then,

(b - a)² = c = a

Given that b = 9, find

(a) the length of a,

(b) the ratio b / c

Does it make more sense & look easier now?