Question

In the given figure, a triangle $A^{\prime }B{C}^{\prime }$ is constructed similar to $\Delta ABC$. The scale factor will be

• A. $\frac{5}{6}$
• B. $1$
• C. $\frac{6}{5}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{5}{6}$


$B_5{C}^{\prime }||B_{6}C$
$\frac{B{B}_5}{B{B}_6}=\frac{B{C}^{\prime }}{BC}=\frac{5x}{6x}$ (By corollary BPT)
$\because \Delta A^{\prime }B{C}^{\prime }\sim \Delta ABC$ (given)
$\frac{A^{\prime }B}{AB}=\frac{A^{\prime }{C}^{\prime }}{AC}=\frac{B{C}^{\prime }}{BC}=\frac{5}{6}$
$\therefore$ Scale factor $=\frac{5}{6}$