Question

PQR is triangle having all sides equal. Point A is on QR such that AR = QR / 3 Find PA if PQ = 6 cm​

Answer 1

Step-by-step explanation:

Answer

Given that:

QP=8cm,PR=6cm and SR=3cm

(I) In △PQR and △SPR

∠PRQ=∠SRP (Common angle)

∠QPR=∠PSR (Given that)

∠PQR=∠PSR (Properties of triangle )

∴△PQR∼△SPR (By AAA)

(II)

SP

PQ

=

PR

QR

=

SR

PR

(Properties of similar triangles)

⇒

SP

8cm

=

3cm

6cm

⇒SP=4cm and

⇒

6cm

QR

=

3cm

6cm

⇒QR=12cm

(III)

ar(△SPR)

ar(△PQR)

=

SP

2

PQ

2

=

4

2

8

2

=4

Answer 2

Answer:

√32

Step-by-step explanation:

qr=6cm (since pq =qr=pr)

now ar=qr/3=2

so pa=√6^2 -2^2

=√32=4√2