Question

Figure $1$ is dilated with a scale factor of $0.5$ about the origin to get figure $2$. The length of b is $2.95$ centimeters and the length of f is $1$ centimeter. The perimeter of figure $1$ is $7.62$ centimeters. Find the value of $d$.

• A. $1.345$ cm
• B. $1.335$ cm
• C. $0.745$ cm
• D. $2.345$ cm

Answer 1

The correct option is B $1.335$ cm

Dilation factor $=0.5$
$b=2.95$ cm
$e=0.5\times 2.95=1.475$ cm
$f=1$ cm
Perimeter of $\Delta ABC=7.62$ cm
Perimeter of $\Delta DEF=0.5\times 7.62=3.81$ cm
Perimeter of $\Delta DEF=e+f+d$(Substituting $3.81$ for the perimeter, $1.476$ for e, and $1$ for f)
$\Rightarrow 3.81=1.475+1+d$
$\Rightarrow 3.81=2.475+d$
$\Rightarrow d=3.81-2.475$
$\Rightarrow d=1.335$ cm