In the △PQR, PQ = 39 in, PR = 17 in, and the altitude PN = 15 in. Find QR. Consider all cases.

QR = 28 inches or 44 inches

Step-by-step explanation:

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.