Answer
QR = 28 inches or 44 inches
explain.
In right triangle QNP, the length of QN is given by the Pythagorean theorem as ...
QP² = QN² +PN²
QN = √(QP² -PN²) = √(1521 -225) = √1296 = 36
In right triangle RNP, the length of RN is similarly found:
RN = √(RP² -PN²) = √(289 -225) = √64 = 8
So, we have N on line QR with QN = 36 and RN = 8.
If N is between Q and R, then ...
QR = QN +NR = 36 +8 = 44
If R is between Q and N, then ...
QR = QN -NR = 36 -8 = 28
The possible lengths of QR are 28 in and 44 in