The perimeter of the given rhombus, with diagonals of 8 cm and 10 cm, is 25.61 cm. This is determined by finding the side length using the Pythagorean theorem and then multiplying it by 4.
To determine the perimeter of a rhombus, recognize that all its sides are of equal length. Given diagonals of 8 cm and 10 cm, designate the length of each side as "s."
The diagonals bisect each other at right angles, creating four congruent right-angled triangles. Applying the Pythagorean theorem, the side length can be found:
s = √((d₁/2)² + (d₂/2)²)
For this rhombus:
s = √((8/2)² + (10/2)²)
s = √(16 + 25)
s = √41
Thus, each side measures √41 cm.
The perimeter (P) of a rhombus is four times the side length:
P = 4s
P = 4 × √41
P = 25.61
Therefore, the perimeter of the rhombus is 25.61 cm.