A metal strip has width 'x' cm. When 2 such metal strips are placed one over…

Concept: When identical strips are placed directly on top of one another, stacking only extends the dimension along which they are piled — here, the combined height of the stack. It adds nothing to the width, the dimension measured across a single strip, because no strip is placed alongside another to widen the arrangement.

Application: Each strip has width x. Stacking 2 strips one over the other changes only the piled dimension (the combined height becomes y); the width of the pile is still exactly the width of one strip. This holds for any number of strips: when z strips are placed in the same manner, the width of the whole arrangement remains x — it does not grow with z, and it does not depend on y.

• zx assumes the width multiplies by the number of strips, as though each stacked strip were placed alongside the previous one instead of directly above it.

• (y – x) assumes the width can be recovered by subtracting the width from the combined height, mixing two dimensions that have no such subtractive relationship.

• (z – 1) x assumes the width grows with every additional strip beyond the first, as though stacking adds width the way placing strips side by side would.

Cross-check: for z = 1 (a single strip, no stacking at all), the width must trivially be x — the relationship ‘width = x, independent of z’ correctly reduces to x in this base case, confirming the width of the arrangement stays x for any number of stacked strips.