Question

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.​

Answer 1

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.