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      Question

      Ratio of perimeter of rectangle and length of rectangle

      was given - 17:5. Quantity I: then area of square whose side is half of rectangle's perimeter Quantity II: twice the perimeter of the rectangle.
      A Quantity I > Quantity II Correct Answer Incorrect Answer
      B Quantity I < Quantity II Correct Answer Incorrect Answer
      C Quantity I ≥ Quantity II Correct Answer Incorrect Answer
      D Quantity I ≤ Quantity II Correct Answer Incorrect Answer
      E Quantity I = Quantity II or no relation can be established Correct Answer Incorrect Answer

      Solution

      ATQ, Let perimeter = P, length = L. Given: P : L = 17 : 5 → P = 17k, L = 5k (k > 0) Quantity I: Side of square = P/2 = 17k/2 Area = (17k/2)² = 289k²/4 Quantity II: 2P = 2 × 17k = 34k Compare: 289k²/4 ? 34k Multiply by 4: 289k² ? 136k Divide by k (>0): 289k ? 136 If k < 136/289 → Q1 < Q2 If k = 136/289 → Q1 = Q2 If k > 136/289 → Q1 > Q2 Since k is not fixed, the relation between Q1 and Q2 cannot be determined.

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