Find the side of the rhombus if its diagonals are 5 m and 12 m.

A rhombus is a parallelogram in which all sides are equal.
The rhombus has its own properties. Based on the properties of the rhombus, knowing the diagonals, we can find the side of the rhombus:
The sum of the squares of the diagonals is equal to the square of the side times 4:
d1² + d2² = 4a²,
where d1 and d2 are the diagonals of the rhombus, and is the side of the rhombus.
We know the diagonals of the rhombus from the problem statement. Substituting their values into the formula, we find the side of the rhombus, solving the equation with one unknown:
5² + 12² = 4 × a²,
4 × a² = 25 + 144,
4 × a² = 169,
a² = √ (169: 4),
a² = √42.25,
a = 6.5.
Answer: the side of the rhombus is 6.5 m.