Question

Figure 1 is dilated with a scale factor of $0.5$ about the origin to get figure 2. The length of b is $26.7cm$ and the length of f is $10cm.$ The perimeter of figure 1 is $76.2cm$. Find the value of d.

• A. $7.5cm$
• B. $23.35cm$
• C. $13.35cm$
• D. $14.75cm$

Answer 1

The correct option is D $14.75cm$

Dilation factor $=0.5$
$b=26.7cm$
$e=0.5\times 26.7=13.35cm$
$f=10cm$
Perimeter of $△ABC=76.2cm$
Perimeter of $△DEF=0.5\times 76.2=38.1cm$
Perimeter of $△DEF=e+f+d$
(substituting $38.1$ for perimeter, $13.35$ for e and $10$ for $f$)
$\Rightarrow 38.1=13.35+10+d$
$\Rightarrow 38.1=23.35+d$
$\Rightarrow d=38.1-23.35$
$\Rightarrow d=14.75cm$

Hence, the correct answer is option A.