Question

    A rectangle has a length to breadth ratio of 7:5. The

    length is increased by 15% without any change to the breadth, resulting in an 84 m² increase in the rectangle's area. What is the perimeter of the original rectangle?
    A 96 metres Correct Answer Incorrect Answer
    B 144 metres Correct Answer Incorrect Answer
    C 120 metres Correct Answer Incorrect Answer
    D 72 metres Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let length and breadth of the rectangle is 7x metres and 5x metres respectively. Area of rectangle = 7x × 5x = 35x2 m2 When length is increased, area of the rectangle = 1.15 × 7x × 5x = 40.25x2 m2 According to question; 40.25x2 – 35x2 = 84 Or, 5.25x2 = 84 Or, x2 = 16 x = 4 Perimeter of the rectangle = 2 × (7 + 5) × 4 = 96 metres

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