Let's look at Nostromo's measurement of Sulaco's length from the perspective of the pancake-loving crew of Sulaco.
Since Nostromo makes an indelible record of the measurement results (permanently stopping the clock or writing the results in a logbook), Sulaco's crew will be able to learn what Nostromo measured (communicating by radio, for example). They can compare the results with the Sulaco length they measure in their own (Sulaco's) rest frame.
Of course, both of Nostromo's measurement techniques are seen by Sulaco's crew to yield the same answer.
During the single-clock measurement, Sulaco's crew can measure the Sulaco's length by seeing how long it takes the (moving) Nostromo clock to coast past the stationary Sulaco. Keep in mind that moving clocks tick slowly...
I'm only showing Nostromo's clock-- not the whole ship-- in the following diagram.
Less time passes on Nostromo's clock than on Sulaco's clocks since moving clocks tick slowly: .
For example, v = 0.8c yields Dt = 0.6 Dt´.
Nostromo measures Sulaco's length to be shorter than Sulaco does, by a factor of .
In general, any/all measurements of the length of a moving object will show it to be shorter by a factor of than a measurement of the object when it is at rest.
This is called Lorentz