To find the length of one side of the rhombus, we can use the properties of a rhombus and the Pythagorean theorem. In a rhombus, the diagonals bisect each other at right angles.
Given the lengths of the diagonals ef = 16 and fh = 12, we first find their half-lengths. The half-lengths of the diagonals are:
- Half of ef = 16 / 2 = 8
- Half of fh = 12 / 2 = 6
Now, we can form a right triangle using these half-lengths as the two legs of the triangle. The length of one side of the rhombus will be the hypotenuse of this right triangle.
Using the Pythagorean theorem:
c² = a² + b²
Where:
- c = length of one side of the rhombus
- a = half of ef = 8
- b = half of fh = 6
Substituting the values:
c² = 8² + 6²
c² = 64 + 36
c² = 100
c = √100
c = 10
Therefore, the length of one side of the rhombus is 10 units.