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.
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