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    Question

    The length of the diagonal of a rhombus is 24 cm, and the perimeter is 80 cm. Find the area of the rhombus.

    A 420 cm² Correct Answer Incorrect Answer
    B 344 cm² Correct Answer Incorrect Answer
    C 384 cm² Correct Answer Incorrect Answer
    D 380 cm² Correct Answer Incorrect Answer

    Solution

    Let the side of the rhombus be a. Given: Perimeter = 80 cm, so 4a = 80 a = 20 cm. Let the diagonals of the rhombus be d₁ = 24 cm and d₂. We know that the diagonals of a rhombus bisect each other at right angles, so we can use Pythagoras' theorem: a² = (d₁/2)² + (d₂/2)² 20² = (24/2)² + (d₂/2)² 400 = 12² + (d₂/2)² 400 = 144 + (d₂/2)² (d₂/2)² = 256 d₂/2 = 16, so d₂ = 32 cm. Area of the rhombus = 1/2 × d₁ × d₂ Area = 1/2 × 24 × 32 = 384 cm². Correct option: C) 384 cm²

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