In a rhombus, the diagonals bisect each other at right angles. Given the lengths of the diagonals, we can find the length of one side of the rhombus.
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The lengths of the diagonals are given as:
- \( QS = 30 \)
- \( RT = 16 \)
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Since the diagonals bisect each other at point \( U \), we can find the lengths of the half-diagonals:
- \( QU = \frac{QS}{2} = \frac{30}{2} = 15 \)
- \( RU = \frac{RT}{2} = \frac{16}{2} = 8 \)
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Now, we can use the right triangle \( QUR \) to find the length of the side \( QR \) of the rhombus using the Pythagorean theorem: \[ QR = \sqrt{QU^2 + RU^2} \] Substituting the values: \[ QR = \sqrt{15^2 + 8^2} \] \[ QR = \sqrt{225 + 64} \] \[ QR = \sqrt{289} \] \[ QR = 17 \]
Thus, the length of one of the sides of the rhombus is \( 17 \).
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