In a rectangle, opposite sides are equal in length. Given that PR and PT represent the lengths of two sides, we can set these two expressions equal to each other to find the value of \( u \).
The equations given are:
- \( PR = 3u - 48 \)
- \( PT = u + 4 \)
Since PR and PT are lengths of opposite sides in rectangle QRST, we can set up the equation:
\[ 3u - 48 = u + 4 \]
Now, we can solve for \( u \):
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Subtract \( u \) from both sides: \[ 3u - u - 48 = 4 \] \[ 2u - 48 = 4 \]
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Add 48 to both sides: \[ 2u = 4 + 48 \] \[ 2u = 52 \]
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Divide both sides by 2: \[ u = \frac{52}{2} \] \[ u = 26 \]
Thus, the value of \( u \) is \( \boxed{26} \).
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