Question

$\Delta ABC\sim \Delta PQR.$ If area$\left(ABC\right)=2.25m^2$, area$\left(PQR\right)=6.25m^2$, $PQ=0.5m$, then length of AB is:

• A. 30 cm
• B. 0.5 m
• C. 50 cm
• D. 3 m

Answer 1

The correct option is A 30 cm

$△ABC\sim △DEF$

In two similar triangles, the ratio of their areas is the square of the ratio of their sides

$\Rightarrow \frac{ar\left(ABC\right)}{ar\left(PQR\right)}={\left(\frac{AB}{PQ}\right)}^2\Rightarrow \frac{2.25}{6.25}={\left(\frac{AB}{.5}\right)}^2\Rightarrow \frac{AB}{.5}=\frac{15}{25}\Rightarrow AB=.3m\Rightarrow AB=.3\times 100=30cm$