The area of a rhombus is given by the formula A = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.

Let’s assume that the diagonals of the rhombus are d1 and d2, and the altitude is h.

Since the diagonals of a rhombus bisect each other at right angles, we can use the Pythagorean theorem to find the lengths of the diagonals.

Using the given perimeter, we can find the length of one side of the rhombus by dividing the perimeter by 4: s = 28 / 4 = 7 m.

Now, let’s consider one half of the rhombus. It can be divided into two right-angled triangles, each with a base of s/2 = 7/2 = 3.5 m and a height of h.

Using the Pythagorean theorem, we can find the length of one diagonal:

d1^2 = (s/2)^2 + h^2 d1^2 = (3.5)^2 + h^2 d1^2 = 12.25 + h^2

Similarly, we can find the length of the other diagonal:

d2^2 = (s/2)^2 + h^2 d2^2 = (3.5)^2 + h^2 d2^2 = 12.25 + h^2

Since the diagonals of a rhombus are perpendicular bisectors of each other, they are equal in length. Therefore, we can equate the two equations:

12.25 + h^2 = 12.25 + h^2

Simplifying, we get:

0 = 0

This equation is true for any value of h. Therefore, the altitude of the rhombus can be any value.

In conclusion, the altitude of the rhombus cannot be determined accurately with the given information.