Question

Both triangles are similar by $SAS$ similarity rule. Find the ratio by which they are similar.

• A. $1:3$
• B. $2:3$
• C. $1:4$
• D. $3:2$

Answer 1

The correct option is A $1:3$

By $SAS$ Rule, $△ABC\cong △PQR$

Two sides and one angle are proportional

$AB\sim PQ$ and $BC\sim QR$

$\Rightarrow \frac{AB}{PQ}=\frac{12}{36}$ and $\frac{BC}{QR}=\frac{15}{45}$

$\Rightarrow \frac{AB}{PQ}=\frac{BC}{QR}=\frac{1}{3}$

$\therefore$ The ratio in which they are similar $=1:3$