# The area of the rhombus is 27 and the perimeter is 36. Find the height of the rhombus.

August 31, 2021 | education

| 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.

From here

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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