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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# 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 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,

hÂ² = 12Â² + 16Â² = 400.

âˆ´ The length of the side of the rhombus is 20 cm.

area of a rhombus = Â½Ã—d1Ã—d2

are of a rhombus= base Ã— height

âˆ´ comparing both formulas

Â½Ã—24Ã—32 = 20Ã—h (base is side of the rhombus)

âˆ´ h= 19.2 cm.

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.Î”AOB by Pythagoras theorem we have

ABÂ²=OAÂ²+OBÂ²

=(12)Â²+(16)Â²

=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

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 inÂ rhombus ABCD.

Using Pyhagoras Theorem for the right-angled triangle ABO,

hÂ² = 12Â² + 16Â² = 400.

âˆ´ The length of the side of the rhombus is 20 cm.

area of a rhombus = Â½Ã—d1Ã—d2

are of a rhombus= base Ã— height

âˆ´ comparing both formulas

Â½Ã—24Ã—32 = 20Ã—hÂ Â Â (base is side of the rhombus)

âˆ´ h= 19.2 cm.