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      Question

      Consider a rectangle where the length to breadth ratio

      is 4:3. Given that the area of the rectangle is 48 cm², a square is constructed using the rectangle's diagonal as its side. Calculate the perimeter of this square.
      A 28 cm Correct Answer Incorrect Answer
      B 40 cm Correct Answer Incorrect Answer
      C 56 cm Correct Answer Incorrect Answer
      D 64 cm Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the length and the breadth of the rectangle be '4a' cm and '3a' cm ATQ, Area of the rectangle = length X breadth 48 = (4a X 3a) Or, a2 = (48/12) = 4 So, 'a' = ±2 But length can't be negative, so 'a' = 2. Length of diagonal of the rectangle = {(length) 2 + (breadth) 2 }1/2 Length of the diagonal of the rectangle = {(4a) 2 + (3a)2}1/2 = (25a2) 1/2 = 5a = 10 cm So, side of the square = length of diagonal of rectangle = 10 cm Therefore, perimeter of the square = (4 X 10) cm = 40 cm 

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