wiz-icon
MyQuestionIcon
MyQuestionIcon
11
You visited us 11 times! Enjoying our articles? Unlock Full Access!
Question

An isosceles triangle PQR, as given, in which the angle bisector PS intersects the line QR at S. Also, PQ=PR and QS=5 cm. Find the length of QR.

A
5 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
10 cm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
15 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Cannot be determined.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 10 cm
The given triangle is as follows:

Let us consider PQS and PRS.

PS is common in both, and as PS is angle bisector of P
So, QPS=RPS
And PQ=PR (Given)

So,PQSPRS
(by Side - Angle - Side)

Now, QS=RS (by corresponding parts of congruent triangles)

So, RS=5cm
And, QR=QS+RS
QR=5 cm+5 cm
QR=10 cm

Hence, option(b) correct.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Side Angle Side or S-A-S Congruence
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon