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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.
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.
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