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Omni-MATH / What is the length of SR if in △PQR, PS is perpendicular to QR, RT is perpendicular to PQ, PT=1, TQ=4, and QS=3?

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problem

What is the length of SRSR if in △PQR\triangle PQR, PSPS is perpendicular to QRQR, RTRT is perpendicular to PQPQ, PT=1PT=1, TQ=4TQ=4, and QS=3QS=3?
Plain-text mathematical notation (without MathML)
What is the length of SR if in △PQR, PS is perpendicular to QR, RT is perpendicular to PQ, PT=1, TQ=4, and QS=3?
Original LaTeX notation
What is the length of $SR$ if in $\triangle PQR$, $PS$ is perpendicular to $QR$, $RT$ is perpendicular to $PQ$, $PT=1$, $TQ=4$, and $QS=3$?

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