In the figure, PT is the altitude of the triangle PQR in which PQ = 25cm,
PR = 17cm and PT = 15cm. If QR = x cm, calculate QR.
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Answer:
From the figure, we have QR=QT+TR.
To find : QT and TR.
In the right angled triangle PTQ,
∠PTQ=90
o
[PT is attitude]
By Pythagoras Theorem, PQ
2
=PT
2
+QT
2
∴PQ
2
−PT
2
=QT
2
∴QT
2
=25
2
−15
2
=625−225=400 ...(1)
Similarly, in the right angled triangle PTR,
by Pythagoras Theorem, PR
2
=PT
2
+TR
2
∴TR
2
=PR
2
−PT
2
=17
2
−15
2
=289−225=64
TR=
64
=8cm ...(2)
From (1) and (2)
QR = QT + TR = 20 + 8 = 28 cm.
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