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    Question

    The perimeter of a rhombus is 50 m. If one of its

    diagonals is 7 m, then the area of the rhombus is
    A 546 m² Correct Answer Incorrect Answer
    B 210 m² Correct Answer Incorrect Answer
    C 504 m² Correct Answer Incorrect Answer
    D 84 m² Correct Answer Incorrect Answer
    E 630 m² Correct Answer Incorrect Answer

    Solution

    Using formula, Perimeter of rhombus = 2 √(d1² + d2²) Where d1 & d2 are diagonals Therefore 2 √(d1² + d2²) = 50 ⇒ √(d1² + d2²) = 25 Squaring both sides, ⇒ (d1² + d2²) = 625 ⇒ 7² + d2² = 625 ⇒ 49 + d2² = 625 ⇒ d2² = 625 – 49 = 576 Therefore, d2 = √576 = 24 Therefore, area of the rhombus = 1/2 x d1 x d2 ⇒ 1/2 x 7 x 24 = 84 m²

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