Question

ΔABC~ΔPQR and AB:PQ=3:4. If AB=9 cm then PQ=___.

A) 5cm

B) 16cm

C) 25cm

D) 12cm

​

Answer 1

Step-by-step explanation:

Since, △ABC is enlarged to △PQR

hence, △ABC∼△PQR

or ratio of sides =

PQ

AB

=

QR

BC

=

PR

AC

ratio of sides =

PQ

6

=

18

12

=

PR

8

ratio of sides =

3

2

and PQ=9 cm and PR=12 cm

Answer 2

Given,

ΔABC~ΔPQR and AB:PQ=3:4. If AB=9 cm then PQ=___.

A) 5cm

B) 16cm

C) 25cm  

D) 12cm

Solution,

Know that in similar triangles the sides are in constant proportion.

Therefore,

$\[\begin{array}{l} \Rightarrow \frac{{AB}}{{PQ}} = \frac{3}{4}\\ \Rightarrow \frac{9}{{PQ}} = \frac{3}{4}\\ \Rightarrow PQ = \frac{4}{3} \times 9\\ \Rightarrow PQ = 12\end{array}\]$

Hence, the correct option is (D) i.e. $\[12{\rm{cm}}.\]$