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In triangle PQR, PQ=39in, PR=17in, and the height PN=15in. Find QR. Consider all possible cases.

Sagot :

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

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