In a rhombus, all sides are equal in length, and the diagonals bisect each other at right angles.
Given:
- The length of diagonal \( LO = 5 \) units
- The length of diagonal \( MO = 8 \) units
Since the diagonals bisect each other, we can find half of each diagonal:
- Half of diagonal \( LO \) is \( \frac{5}{2} = 2.5 \) units
- Half of diagonal \( MO \) is \( \frac{8}{2} = 4 \) units
Now, we can use the Pythagorean theorem to find the length of one side of the rhombus, \( LM \). The lengths of the two halves of the diagonals \( LO \) and \( MO \) form a right triangle with side \( LM \):
\[ LM^2 = (2.5)^2 + (4)^2 \] \[ LM^2 = 6.25 + 16 \] \[ LM^2 = 22.25 \] \[ LM = \sqrt{22.25} \approx 4.72 \text{ units} \]
So, the length of side \( LM \) is approximately \( 4.72 \) units.
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