Question

In △ABC, AB = 3cm,BC = 4cm and AC = 4.5cm.△PQR~△ABC,
QR = 8cm. What is the perimeter of △PQR?​

Answer 1

Step-by-step explanation:

tr. PQR ~ tr. ABC

By CPST,

\begin{gathered}\frac{PQ}{AB} = \frac{QR}{BC}=\frac{RP}{CA}\\= > \frac{4}{8}= \frac{1}{2} = \frac{6}{BC}=\frac{5}{CA}\end{gathered}

AB

PQ

=

BC

QR

=

CA

RP

=>

8

4

=

2

1

=

BC

6

=

CA

5

=>BC = 12cm.

=>CA = 10cm.

So,

Perimeter of triangle ABC

= 8+10+12 = 30cm.

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Answer 2

Step-by-step explanation:

∆ABC ~∆POR

therefore, AB/PQ =BC/QR =AC/PR

Given that,

QR=8

Therefore, BC/ QR=4/8=1/2

So, AB/PQ=1/2. [since, AB/PQ=BC/QR]

=> 3/PQ=1/2

=> PQ=6 cm

Similarly,

AC/PR= 1/2

=> 4.5/PR=1/2

=> PR= 9

Therefore, PERIMETER OF ∆PQR=( 6+8+9)cm

=23cm

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