To find the length of one of the sides of rhombus QRST, we can use the properties of a rhombus and the relationship between its diagonals and sides.
In a rhombus, the diagonals bisect each other at right angles. Given the lengths of the diagonals:
- \( QS = 30 \)
- \( RT = 16 \)
We can find the lengths of the segments created by these diagonals at their intersection point \( U \):
- \( QU = \frac{QS}{2} = \frac{30}{2} = 15 \)
- \( RU = \frac{RT}{2} = \frac{16}{2} = 8 \)
Now, using the Pythagorean theorem, we can calculate the length of one side of the rhombus (let's call it \( s \)). In triangle \( QUR \):
\[ s^2 = QU^2 + RU^2 \]
Substituting the values of \( QU \) and \( RU \):
\[ s^2 = 15^2 + 8^2 \]
Calculating this:
\[ s^2 = 225 + 64 = 289 \]
Now taking the square root:
\[ s = \sqrt{289} = 17 \]
Thus, the length of one of the sides of the rhombus is 17.
So the correct answer is 17.
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