The area of the rhombus is = 10 and the perimeter is 20. Find the height of the rhombus.

Let’s write down the definition of a rhombus: “A rhombus is a parallelogram in which all sides are equal.”
1) Knowing the perimeter of the rhombus, we find the length of its side.
The perimeter of any geometric shape is the sum of the lengths of all its sides. Let us denote the perimeter by the letter P.
The rhombus has 4 identical sides. Let’s write down the formula for the perimeter of a rhombus:
P = 4 × a.
Let us find side a from the formula:
a = P: 4.
We calculate the length of the side of the rhombus, substituting the value of the perimeter into the formula:
a = 20: 4 = 5.
1) Find the height of the rhombus. Let’s write the formula for the area, knowing the side of the rhombus and the height:
S = ah,
where a is the side of the rhombus, h is the height.
Let us express the height from this formula:
h = S: a.
h = 10: 5 = 2.
Answer: The height of the rhombus is 2.