Question

A rectangle with a width of 2.5 cm and a length of 3 cm is dilated by a scale factor of 4. Which statements about the new rectangle are true?

Check all that apply.

The dimensions of the new rectangle will be 10 cm by 12 cm.
The dimensions of the new rectangle will be 40 cm by 48 cm.
The new perimeter will be 4 times the original perimeter.
The new perimeter will be 16 times the original perimeter.
The new area will be 4 times the original area.
The new area will be 16 times the original area.
The new perimeter will be 44 cm.
The new area will be 30 square cm

Answer 1

A,C,F,G


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Answer 2

• 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.

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=
`4*2.5=10\ cm`

length of new rectangle=
`4*3=12\ cm`

∴The dimensions of the new rectangle will be 10 cm by 12 cm.

Now, Perimeter of original rectangle=
`2(l+w)=2(3+2.5)=2(5.5)=11\ cm`

Thus, Perimeter of new rectangle=
`2(4l+4w)=2(12+10)=2(22)=44\ cm`

⇒ Perimeter of new rectangle=44 cm=
`4*11\ cm`

∴The new perimeter will be 4 times the original perimeter.

Now, Area of original rectangle=
`lw=3*2.5=7.5\ cm^2`

Thus, Area of new rectangle=
`4l*4w=12*10=120\ cm^2`

Area of new rectangle=
`16lw=16(lw)`

⇒The new area will be 16 times the original area.