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

Solution:

In the △PQR, PQ = 39in, PR = 17in, and the altitude PN = 15in.

Then angle PNQ = 900

Consider right angle triangle PNQ,

By applying Pythagoras theorem,

PQ² = PN² + NQ²

39² = 15² + NQ²

By transforming we get,

NQ² = 39² - 15²

NQ² = 1521 - 225

NQ² = 1296

NQ = √1296

NQ = 36in

Now, consider right angle triangle PNR,

By applying Pythagoras theorem,

PR² = PN² + NR²

17² = 15² + NR²

By transforming we get,

NR² = 17² - 15²

NR² = 289 - 225

NR² = 64

NR = √64

NR = 8in

So, RQ = NQ + NR

On substituting the value of NQ and NR, we get

RQ = 36 + 8

RQ = 44in

Therefore, QR is 44in.

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

Summary:

In the △PQR, PQ = 39in, PR = 17in, and the altitude PN = 15in then the value of QR is 44in.