Question

In $△ABC$, the measures of $\overline{BC},\overline{CA},\overline{AB}$ are in the ratio $3:4:5$. Correspondence $ABC\leftrightarrow PQR$ is congruence. If $PR=12$, then the perimeter of $△PQR$ is .......... .

• A. $12$
• B. $24$
• C. $27$
• D. $36$

Answer 1

Answer: (D)

$36$

In $△ABC$, $\overline{BC}:\overline{CA}:\overline{AB}=3:4:5$

Let the measure of sides $\overline{BC},\overline{CA},\overline{AB}$ of $△ABC$ are $3x,4x$ and $5x$ $(x>0)$ respectively.
Then, Perimeter of $△ABC=3x+4x+5x=12x$
Now, $\frac{\text{Perimeter of}△ABC}{\text{Perimeter of}△PQR}=\frac{AC}{PR}$
$⟹\frac{12x}{\text{Perimeter of}△PQR}=\frac{4x}{12}$
$⟹\text{Perimeter of}△PQR=\frac{12\times 12}{4}$
$\therefore$ Perimeter of $△PQR=36$