Question

$△ABC\sim △PQR$ If ar(ABC)=2.25$m^2$ ar(PQR)=6.25$m^2$, PQ=0.5 m, then length of AB is

• A. $30cm$
• B. $1.5cm$
• C. $50cm$
• D. $2m$

Answer 1

The correct option is A $30cm$

The area of two similar triangles are proportional to the square of their corresponding sides

$\therefore \frac{Ar\left(ABC\right)}{ar\left(PQR\right)}=\frac{(AB{)}^2}{(PQ{)}^2}$

$\Rightarrow \frac{2.25}{6.25}=\frac{(AB{)}^2}{(.5{)}^2}$

$\Rightarrow A{B}^2=\frac{2.25\times .5}{6.25}$

$\Rightarrow A{B}^2=.09$

$\Rightarrow AB=.3m=30cm$