The diagonals of the rhombus are 6 cm and 8 cm. Determine the length of the side of the rhombus.

Let’s use the fact that in any rhombus its diagonals intersect at right angles and are halved by the intersection point.

Consider one of the four triangles that form the sides of the rhombus and its diagonal. All these triangles are equal and are rectangular with legs equal to half the diagonals of this rhombus and a hypotenuse equal to the side of this rhombus.

According to the problem statement, the diagonals of this rhombus are 6 cm and 8 cm.

Therefore, the halves of these diagonals are 4 cm and 3 cm, respectively, and using the Pythagorean theorem, we find the length of the side of this rhombus:

√ (3 ^ 2 + 4 ^ 2) = √ (9 + 16) = √25 = 5 cm.

Answer: the length of the side of the rhombus is 5 cm.