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CTET PAPER I 2021 · PYQ · Mensuration / Perimeter and Area · medium

A wire in the form of a square encloses an area of 144 cm². How much area is enclosed if the same wire is bent in the form of a rectangle of length 16 cm ?

  1. A.124 cm²
  2. B.48 cm²
  3. C.128 cm²✓ Correct
  4. D.96 cm²

Explanation

Area of square = 144 cm², so side = 12 cm. Perimeter of square = 4 × 12 = 48 cm, which is the length of wire. When bent into a rectangle of length 16 cm, perimeter = 2(l + b) = 48, so l + b = 24, giving b = 24 − 16 = 8 cm. Area of rectangle = 16 × 8 = 128 cm².
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