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

1. The perimeter of a polygon is equal to the sum of the lengths of all its sides. Since all four sides of a rhombus are equal, we denote the length of its side as a, then its perimeter is:

P = a + a + a + a = 4 * a.

Substitute the data by the value condition and find the length of the rhombus side:

4 * a = 36;

a = 36/4 (proportional);

a = 9.

2. The area of a rhombus can be found through the length of its side and the length of the height lowered to this side, according to the formula:

S = a * h.

Substitute the data by the value condition and find the length of the rhombus height:

9 * h = 27;

h = 27/9 (in proportion);

h = 3.

Answer: h = 3.