Question

$\Delta ABC\Delta PQR$ for the correspondence $ABC\leftrightarrow PQR$ . If the perimeter of $\Delta ABC$ is $12$ and the perimeter of $\Delta PQR$ is $20$ , then $AB:PQ=$ ______

• A. $\frac{6}{5}$
• B. $\frac{2}{5}$
• C. $\frac{3}{5}$
• D. $\frac{1}{5}$

Answer 1

The correct option is C $\frac{3}{5}$

$ABC\leftrightarrow PQR$

$\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}=k\left(say\right)$

$AB=k\left(PQ\right);AC=k\left(PR\right);BC=k\left(QR\right)$

$[AB+BC+AC]=k[PQ+RQ+PR]$

Perimeter $\left(\Delta ABC\right)$ = perimeter $\left(\Delta PQR\right)\times k$

$12=20\times k$

$k=\frac{12}{20}=\frac{3}{5}$

$\therefore \frac{AB}{PQ}=k=\frac{3}{5}$