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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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.

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

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.