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Rekha wants to run a decorative cord once around a regular pentagon of side 12 cm. Vikas wants to do the same around a square of side 15 cm. Who needs the longer cord?

Class 6MensurationMensuration
  • ARekha, because a pentagon has more sides than a square.
  • BVikas, because his shape has the longer sides.
  • CBoth need exactly the same length of cord.
  • DIt cannot be decided without knowing the areas.

Step-by-Step Solution

Pentagon: cm. Square: cm. The two perimeters are equal, so both need 60 cm. Having more sides does not automatically give a bigger perimeter — the side length matters just as much, and area is not needed here at all.
Answer: C) Both need exactly the same length of cord.

Key idea: Perimeter — the journey around

Imagine an ant walking around the edge of a shape and returning to where it started. The total distance it walks is the perimeter. For any closed shape: **add up every side**. Order doesn't matter; just include each side once.

For a triangle with sides 3, 4, 5: perimeter = 3 + 4 + 5 = 12. For an irregular shape: add every edge.

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