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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

Respuesta :

Answer:

The new perimeter will be 4 times the original perimeter.

The new area will be 4 times the original area.

Step-by-step explanation:

The area and perimeter of new rectangle will be 120 square cm and 44 cm. Then the correct options are A, C, F, and G.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

A rectangle with a width of 2.5 cm and a length of 3 cm is dilated by a scale factor of 4.

L = 3 cm

W = 2.5 cm

Then the new dimension of the rectangle will be

W' = 4 x 2.5 = 10 cm

L' = 4 x 3 = 12 cm

Then the perimeter of the rectangle will be

P = 2(L + W)

Then the perimeter of the new rectangle will be

P = 2(4L + 4W)

P = 4 x 2(L + W)

The new perimeter is the 4 times of original perimeter.

P = 8(2.5 + 3)

P = 44 cm

The area of the rectangle will be

A = L x W

Then the area of the new rectangle will be

A = 4L x 4W

A = 16 x L x W

The new area is the 16 times of original area.

A = 16 x 2.5 x 3

A = 120 square cm

Then the correct options are A, C, F, and G.

More about the dilation link is given below.

https://brainly.com/question/2856466

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