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A four-sided badge has a perimeter of 68 cm. Three of its sides measure 14 cm, 21 cm and 16 cm. How long is the fourth side?

Class 6MensurationMensuration
  • A17 cm
  • B20 cm
  • C34 cm
  • D51 cm

Step-by-Step Solution

Add the three sides you know: 14 + 21 + 16 = 51 cm. The fourth side is what is left of the perimeter: 68 − 51 = 17 cm. 51 cm is only the sum of the given sides, and 34 cm is half the perimeter — halving works only when the sides come in equal pairs, which is not the case for this badge.
Answer: A) 17 cm

Key idea: Perimeter shortcuts for special shapes

**Rectangle**: opposite sides are equal, so perimeter = l + b + l + b = 2(l + b).

**Square**: all four sides equal, so perimeter = 4 × s.

**Equilateral triangle**: all three sides equal, perimeter = 3 × s.

**Regular polygon with n sides of length s**: perimeter = n × s.

These shortcuts are just 'add the sides' written shorter.

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