△ABC has sides AB=5 cm, BC=6 cm, AC=7 cm. △XYZ is congruent to △ABC. What is the perimeter of △XYZ?

Correct — B. Congruent triangles are identical in size and shape, so △XYZ has the same three sides as △ABC.

Match corresponding sides: XY = AB = 5 cm, YZ = BC = 6 cm, XZ = AC = 7 cm
Add all three: 5 + 6 + 7 = 18 cm → option (b)

Why the others are wrong

• (a)
  13 cm — 13 cm is only BC + AC (6 + 7). A perimeter adds all three sides, so AB's 5 cm is missing.
• (c)
  20 cm — 20 cm is 2 cm more than 5 + 6 + 7. Congruence does not change any length, so the perimeter cannot differ from △ABC's 18 cm.
• (d)
  24 cm — 24 cm would need a larger triangle, similar to △ABC but scaled up by 4⁄3. Congruent means a scale factor of 1, so the perimeter stays 18 cm.

Two triangles are congruent when one fits exactly on the other: all three pairs of corresponding sides and all three pairs of corresponding angles are equal.

Anything built from those measures carries across unchanged, so the perimeter and the area are equal too. Similar triangles are different: only the shape matches, and perimeters scale by the ratio of corresponding sides.

Key facts

• Congruent triangles have equal corresponding sides and equal corresponding angles.
• Congruent triangles have equal perimeters and equal areas.
• In △XYZ ≅ △ABC the letter order gives the correspondence: X↔A, Y↔B, Z↔C.
• Similar triangles with side ratio k have perimeters in the ratio k and areas in the ratio k².

Common traps

• Adding only two of the three sides, which gives 11, 12 or 13 cm.
• Reading congruent as similar and looking for a scale factor the question never gives.

No directly related past PYQ was found.