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    Question

    The perimeter of a rhombus is 130 m. If one of its diagonals is 16 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) = 130 ⇒ √(d1² + d2²) = 65 Squaring both sides, ⇒ (d1² + d2²) = 4225 ⇒ 16² + d2² = 4225 ⇒ 256 + d2² = 4225 ⇒ d2² = 4225 – 256 = 3969 Therefore, d2 = √3969 = 63 Therefore, area of the rhombus = 1/2 x d1 x d2 ⇒ 1/2 x 16 x 63 = 504 m²

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