Question

Let $△$ABC ~ $△$PQR. If area(ABC) = 2.25 $m^2$, area(PQR) = 6.25 $m^2$, PQ = 0.5 $m$, then length of AB is:

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

Answer 1

Answer: (A)

30 cm

$\frac{ar\left(ABC\right)}{ar\left(PQR\right)}=\frac{2.25}{6.25}$

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

$\Rightarrow {\left(\frac{AB}{PQ}\right)}^2=\frac{225}{625}\Rightarrow \frac{AB}{PQ}=\frac{15}{25}\Rightarrow \frac{AB}{0.5}=\frac{3}{5}\Rightarrow AB=0.3m\Rightarrow AB=0.3\times 100=30cm$