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,
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.
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.
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Step-by-step explanation:
Triangles : The lengths of the diagonals of a rhombus are 24 cm and 32 cm. Calculate the length of the altitude of the rhombus.
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.
Attachments:
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