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    Question

    The perimeter of a rhombus is 170 m. If one of its

    diagonals is 36 m, then the area of the rhombus is
    A 180 m² Correct Answer Incorrect Answer
    B 1320 m² Correct Answer Incorrect Answer
    C 330 m² Correct Answer Incorrect Answer
    D 336 m² Correct Answer Incorrect Answer
    E 1386 m² Correct Answer Incorrect Answer

    Solution

    Using formula, Perimeter of rhombus = 2 √(d1² + d2²) Where d1 & d2 are diagonals Therefore 2 √(d1² + d2²) = 170 ⇒ √(d1² + d2²) = 85 Squaring both sides, ⇒ (d1² + d2²) = 7225 ⇒ 36² + d2² = 7225 ⇒ 1296 + d2² = 7225 ⇒ d2² = 7225 – 1296 = 5929 Therefore, d2 = √5929 = 77 Therefore, area of the rhombus = 1/2 x d1 x d2 ⇒ 1/2 x 36 x 77 = 1386 m²

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