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    Question

    If the length and breadth of a rectangle are each

    increased by 4 m, its area increases by 224 m². The ratio of the perimeter of the square to that of the rectangle is 1:2. Find the side of the square.
    A 18 m Correct Answer Incorrect Answer
    B 13 m Correct Answer Incorrect Answer
    C 25 m Correct Answer Incorrect Answer
    D 10 m Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let length = x m, breadth = y m (x + 4)(y + 4) – xy = 224 ⇒ 4x + 4y + 16 = 224 ⇒ 4x + 4y = 208 ⇒ x + y = 52 Perimeter of rectangle = 2(x + y) = 104 m Perimeter of square = (1/2) × 104 = 52 m Side of square = 52 ÷ 4 = 13 m

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