The area of the rhombus is
S = ah, where a is the side of the rhombus, h is the height of the rhombus.
Hence, the height of the rhombus is
h = S / a.
All sides of the rhombus are equal, so its perimeter is
P = 4a.
a = P / 4.
Find the side of the rhombus:
a = 36/4 = 9.
Now you can find the height of the rhombus:
h = 27/9 = 3.
Answer: The height of the rhombus is 3.
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