Question

PT is an altitude of the triangle pqr in which PQ equal to 25 cm PR equal to 17 cm PT equal to 15 cm and QR is equal to x cm. calculate x . explain it with full diagram

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.

Step-by-step explanation: