One of the diagonals of a parallelogram is its height and is equal to 9 cm.Find the sides of this parallelogram if its area is 108 cm2

Given: ABCD – parallelogram, AD = 9cm ^ 2, Sabcd = 108cm ^ 2
Search: AB, BD, CD, AC
Decision:
1.S = ah
a = S / h
CD = S / AD
CD = 108/9
CD = 12cm
2. Consider a triangle ACD:
angle 1 = 90 degrees
ACD – rectangular since angle 1 = 90 degrees
3. By the Pythagorean theorem, we find the hypotenuse ACD:
a ^ 2 + b ^ 2 = c ^ 2
AC ^ 2 = AD ^ 2 + CD ^ 2
AC ^ 2 = 9 ^ 2 + 12 ^ 2
AC ^ 2 = 81 + 144
AC ^ 2 = 225
AC = 15cm
4. AC = BD = 15cm by the property of the sides of the parallelogram
CD = AB = 12cm by the property of the sides of the parallelogram
Answer: AB = 12cm, BD = 15cm, CD = 12cm, AC = 15cm.