If △ABC∼△XYZ and AB=4 cm, BC=6 cm, XY=8 cm, what is the length of YZ?

Correct — B. △ABC∼△XYZ pairs the vertices in order: A↔X, B↔Y, C↔Z.

So AB matches XY, and BC matches YZ
Scale factor = XY⁄AB = 8⁄4 = 2
YZ = 2 × BC = 2 × 6 = 12 cm

Check: AB⁄XY = 4⁄8 and BC⁄YZ = 6⁄12, both 1⁄2 ✓ → option (b)

Why the others are wrong

• (a)
  10 cm — 10 cm adds the difference XY − AB = 4 to BC: 6 + 4 = 10. Similar triangles share a ratio, not a difference, so each side is multiplied by 2.
• (c)
  14 cm — 14 cm makes BC⁄YZ = 6⁄14 = 3⁄7, but AB⁄XY = 1⁄2. Matching sides of similar triangles must all be in the same ratio.
• (d)
  16 cm — 16 cm doubles XY (8 × 2) instead of BC. The scale factor carries BC = 6 to its partner YZ, and 2 × 6 = 12.

In similar triangles, corresponding sides are in one fixed ratio, the scale factor, and corresponding angles are equal.

The letter order in △ABC∼△XYZ says which sides correspond: first with first, second with second. So AB↔XY, BC↔YZ and CA↔ZX.

One matched pair gives the ratio. Every other side follows by multiplying.

Key facts

• △ABC∼△XYZ means A↔X, B↔Y, C↔Z, so AB⁄XY = BC⁄YZ = CA⁄ZX.
• Perimeters of similar triangles are in the same ratio as their corresponding sides.
• Areas of similar triangles are in the ratio of the squares of their corresponding sides.

Common traps

• Pairing sides by size instead of by the letter order in the similarity statement.
• Adding the difference between matching sides instead of multiplying by the scale factor.

No directly related past PYQ was found.