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the length of the diagonals of a rhombus are in the ratio 3:4 if one side of the rhombus is 10 cm the length of both the diagonals of the rhombus

  • math -

    By the definition of a rhombus , all sides are equal, so if one side is 10, then all sides are equal to 10.

    Also, the diagonals bisect each other at right angles creating 4 congruent right-angled triangles.

    Looking at one of these triangles, we have sides
    3x, 4x, and hypotenuse 10

    9x^2 + 16x^2 = 100
    25x^2 = 100
    x^2 = 4
    x = 2

    Each triangle is 6 cm by 8 cm by 10 cm
    According to my definitions, the diagonals would be 6x and 8x, or
    12 cm and 16 cm.

  • math -

    Ab=62
    Ad=48

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