The height AH of the rhombus ABCD Divides the side CD into segments DH = 21 and CH = 8 find the height of the rhombus.
Determine the length of the side of the rhombus CD.
CD = DH + CH = 21 + 8 = 29 cm.
Since the lengths of all its sides are equal for a rhombus, AD = AB = CD = CB = 29 cm.
The triangle ADH is rectangular, since AH is the height of the rhombus, then, by the Pythagorean theorem,
AH ^ 2 = AD ^ 2 – DH ^ 2 = 29 ^ 2 – 21 ^ 2 = 841 – 441 = 400.
AH = 20 cm.
Answer: The height of the rhombus is 20 cm.
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