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    Question

    The perimeter of a rhombus is 74 m. If one of its diagonals is 12 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) = 74 ⇒ √(d1² + d2²) = 37 Squaring both sides, ⇒ (d1² + d2²) = 1369 ⇒ 12² + d2² = 1369 ⇒ 144 + d2² = 1369 ⇒ d2² = 1369 – 144 = 1225 Therefore, d2 = √1225 = 35 Therefore, area of the rhombus = 1/2 x d1 x d2 ⇒ 1/2 x 12 x 35 = 210 m²

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