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

To find the height, we first turn to the formulas for the perimeter and area of the rhombus.
S = ah-area of a rhombus;
P = 4a-rhombus perimeter;
By condition, S = 27 and P = 36.
From the formula for the perimeter, we find the expression for the side of the rhombus:
a = P / 4;
Substitute this expression into the area formula:
S = P / 4 * h;
Find the expression for the height:
h = 4S / P;
Substitute numerical values:
h = 4 * 27/36 = 3.