Question

A rectangle has a length of 12 mm and a width of 15 mm. A new rectangle was created by multiplying all of the dimensions by a scale factor of 1 3 . A rectangle with length 12 millimeters and width 15 millimeters. A smaller rectangle with length 4 millimeters and width 5 millimeters. Which statement best describes the change in the perimeter of the new rectangle? The new perimeter will be One-half times the perimeter of the original rectangle. The new perimeter will be One-third times the perimeter of the original rectangle. The new perimeter will be 2 times the perimeter of the original rectangle. The new perimeter will be 3 times the perimeter of the original rectangle.

Answer 1

Answer:

• 4 mm by 5 mm
• 1/3 the perimeter of the original

Step-by-step explanation:

When each of the dimensions is multiplied by 1/3, the result is a rectangle that is ...

   (12 mm)·(1/3) by (15 mm)·(1/3) = 4 mm by 5 mm

The result is ...

  a smaller rectangle with length 4 millimeters and width 5 millimeters

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The perimeter of the smaller rectangle has the same ratio to the original that the side lengths do.

The new perimeter will be 1/3 times the perimeter of the original rectangle.

Answer 2

The change in perimeter of the new rectangle will be 3 times the perimeter of the original rectangle.

What is the perimeter of a rectangle?

For a known length and width of a rectangle, the expression for calculating the perimeter of a rectangle is 2(L × w).

From the given information:

A rectangle's length = 12 mm, and width = 15 mm

• Using a Scale factor of 1 : 3

• A new smaller rectangle's length = 4 mm, and width = 5 mm

Therefore, we can deduce that the change in perimeter of the new rectangle will be 3 times the perimeter of the original rectangle.

This is because by using the scale factor:

$\mathbf{\dfrac{1}{3}(12) \times \dfrac{1}{3}(15)}$

We can get the value for the length and width of the new smaller rectangle as 4 mm and 5 mm respectively.

Learn more about the perimeter of a rectangle here:

https://brainly.com/question/19819849

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