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Deepak Bora
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Triangles : The lengths of the diagonals of a rhombus are 24 cm and 32 cm. Calculate the length of the altitude of the rhombus.

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The lengths of the diagonals of a rhombus are 24 cm and 32 cm. Calculate the length of the altitude of the rhombus.

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  1. This answer was edited.

    The diagonals of a rhombus bisect each-other at right angles,with the side of the rhombus being the hypotenuse . Half the lengths of the diagonals AO = 12 cm , BO= 16 cm. and the hypotenuse(AB) in right triangle ABO in  rhombus ABCD.

    Using Pyhagoras Theorem for the right-angled triangle ABO,

    h² = 12² + 16² = 400.

    ∴ The length of the side of the rhombus is 20 cm.

    area of a rhombus = ½×d1×d2

    are of a rhombus= base × height

    ∴ comparing both formulas

    ½×24×32 = 20×h    (base is side of the rhombus)

    ∴ h= 19.2 cm.

    • 111
  2. Let ABCD be a rhombus with AC and BD as its diagonals.
    We know that the diagonals of a rhombus bisect each other at right angles.
    Let O be the intersecting point of both the diagonals.
    Let AC=24cm and BD=32cm
    OA=AC/2
    OA= 24/2=12cm
    OB=BD/2
    OB=32/2=16cm
    In rt.ΔAOB by Pythagoras theorem we have
    AB²=OA²+OB²
    =(12)²+(16)²
    =144+256
    =400
    AB=20cm
    Hence, each side of the rhombus is of length 20cm
    Area of rhombus=1/2*AC*BD
    =1/2*24*32
    =12*32
    Area of rhombus=base*altitude
    12*32=20*h
    19.2cm=h

    • 16
  3. The diagonals of a rhombus bisect each-other at right angles,with the side of the rhombus being the hypotenuse . Half the lengths of the diagonals AO = 12 cm , BO= 16 cm. and the hypotenuse(AB) in right triangle ABO in rhombus ABCD.

    Using Pyhagoras Theorem for the right-angled triangle ABO,

    h² = 12² + 16² = 400.

    ∴ The length of the side of the rhombus is 20 cm.

    area of a rhombus = ½×d1×d2

    are of a rhombus= base × height

    ∴ comparing both formulas

    ½×24×32 = 20×h (base is side of the rhombus)

    ∴ h= 19.2 cm.

    • 3
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