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17 July, 19:51

A rhombus has side lengths of 25. What could be the lengths of the diagonals?

A. 22 and 40

B. 26 and 36

C. 26 and 48

D. 30 and 40

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Answers (1)
  1. 17 July, 22:00
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    The correct option is;

    D. 30 and 40

    Step-by-step explanation:

    Here, we have that the rhombus is a quadrilateral with equal and parallel sides hence the length of the diagonals will be

    2 * 25*sinθ and 2 * 25 * cosθ

    Therefore tanθ = (2 * 25*sinθ) / (2 * 25 * cosθ) = (sinθ) / (cosθ)

    Therefore, the root of the sum squares of both diagonals = 50

    Therefore, we analyze each of the options as follows

    For A. we have √ (22² + 40²) = 45.65 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

    For B. we have √ (26² + 36²) = 44.41 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

    For C. we have √ (26² + 48²) = 55.59 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

    For D. we have √ (30² + 40²) = 50 therefore these are possible lengths of diagonals of the rhombus in question.
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