Answer:
- The dimensions of the new rectangle will be 10 cm by 12 cm.
- The new perimeter will be 4 times the original perimeter.
- The new area will be 16 times the original area.
- The new perimeter will be 44 cm.
Step-by-step explanation:
Given dimensions of original rectangle , length(l)=3 cm and width(w)=2.5 cm
We know that after dilation with scale factor (k), the dimension of new figure = k times the original dimensions.
Thus width of new rectangle=[tex]4\times2.5=10\ cm[/tex]
length of new rectangle=[tex]4\times3=12\ cm[/tex]
∴The dimensions of the new rectangle will be 10 cm by 12 cm.
Now, Perimeter of original rectangle=[tex]2(l+w)=2(3+2.5)=2(5.5)=11\ cm[/tex]
Thus, Perimeter of new rectangle=[tex]2(4l+4w)=2(12+10)=2(22)=44\ cm[/tex]
⇒ Perimeter of new rectangle=44 cm=[tex]4\times11\ cm[/tex]
∴The new perimeter will be 4 times the original perimeter.
Now, Area of original rectangle=[tex]lw=3\times2.5=7.5\ cm^2[/tex]
Thus, Area of new rectangle=[tex]4l\times4w=12\times10=120\ cm^2[/tex]
Area of new rectangle=[tex]16lw=16(lw)[/tex]
⇒The new area will be 16 times the original area.
