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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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
19.2 cm = h
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