Question

A PQR is an equilatral triangle. Point S is on seg QR such that QS = 1/3 QR. Prove that : 9 PS² = 7 PQ²​

Answer 1

Step-by-step explanation:

PT be the perpendicular from P on QR. Hence,QT=

2

1

QR

ST=QR(

2

1

−

3

1 )=

6

1QR

PS

2

=PT

2

+ST

2also,PT=QTtan60

∘PT=

3

QT

PS

2

=3QT

2

+

36

QR

2

PS

2

=

4

3QR

2

+

36

QR

2

PS

2

=

36

28QR

2

=

9

7QR

2

QR=PQ

9PS

2

=7PQ

2