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    Question

    The perimeter of a rectangle is 100 m, and its diagonal

    is 41 m. Find the area of the rectangle.
    A 409.5 m² Correct Answer Incorrect Answer
    B 360.5 m² Correct Answer Incorrect Answer
    C 420.5 m² Correct Answer Incorrect Answer
    D 320 m² Correct Answer Incorrect Answer

    Solution

    Let the length and breadth of the rectangle be l and b. Perimeter = 2(l + b) = 100 → l + b = 50. Diagonal = sqrt(l² + b²) = 41. Using (l + b)² = l² + b² + 2lb: 50² = 41² + 2lb. 2500 = 1681 + 2lb. 2lb = 819  lb = 409.5. Area = l × b = 409.5 m². Correct Option: a

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