Question

16. IF APQR ~ AABC, PQ=6 cm, AB = 8 cm and perimeter of AABC is 36 cm, then perimeter
of APQR is
(a) 20.25 cm
(b) 27 cm
(c) 48 cm
(d) 64 cm
​

Answer 1

Step-by-step explanation:

if two triangle are similar then

perimeter of PQR/perimeter of ABC=PQ/AB

X/36=6/8

X=27 cm

Answer 2

If ∆PQR ~ ∆ABC, then perimeter of ∆PQR is 27 cm.

Option (b) is correct.

Given:

• ∆PQR ~ ∆ABC
• PQ=6 cm, AB = 8 cm
• Perimeter of ∆ABC is 36 cm

To find:

Perimeter of ∆PQR is

(a) 20.25 cm

(b) 27 cm

(c) 48 cm

(d) 64 cm

Solution:

When two triangles are similar than ratio of their corresponding sides and ratio of their perimeters are equal.

Step 1:

Write given terms

PQ= 6 cm

AB= 8 cm

Ratio of corresponding sides are equal.

Thus,

$\frac{PQ}{AB} = \frac{QR}{CB} = \frac{PR}{AC} = \frac{6}{8}$

or

$\frac{PQ}{AB} = \frac{QR}{CB} = \frac{PR}{AC} = \frac{3}{4}$

Step 2:

Ratio of perimeters are also equal.

$\frac{PQ+QR+PR}{AB+CB+AC} = \frac{3}{4}$

put value of denominator, ie perimeter of ∆ABC.

$\frac{PQ+QR+PR}{36} = \frac{3}{4}$

or

$PQ+QR+PR = \frac{3 \times 36}{4}$

or

$PQ+QR+PR =27\: cm$

Thus,

Perimeter of ∆PQR is 27 cm.

Option b is correct.

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