In a rhombus, the diagonals bisect each other at right angles. Therefore, we can use the lengths of the diagonals to find the sides of the rhombus.
Given:
- \( QS = 30 \) (diagonal)
- \( RT = 16 \) (diagonal)
First, we can find the half-lengths of the diagonals:
- \( QU = \frac{QS}{2} = \frac{30}{2} = 15 \)
- \( RU = \frac{RT}{2} = \frac{16}{2} = 8 \)
Now, we can apply the Pythagorean theorem to find the length of one side of the rhombus (let's call the side \( s \)): \[ s^2 = QU^2 + RU^2 \] \[ s^2 = 15^2 + 8^2 \] \[ s^2 = 225 + 64 \] \[ s^2 = 289 \] \[ s = \sqrt{289} \] \[ s = 17 \]
Therefore, the length of one side of the rhombus is \( 17 \).
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