Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 06, 2024

A figure has a perimeter of $16$ units. What is the perimeter after a dilation with a scale factor of $8$ ?

STEP 1

Assumptions
1. The original perimeter of the figure is 16 units.
2. The figure undergoes a dilation with a scale factor of 8.
3. The dilation affects all dimensions of the figure proportionally.

STEP 2

Understand how dilation affects the perimeter of a figure. Dilation by a scale factor means that all linear dimensions of the figure are multiplied by the scale factor.

STEP 3

Apply the scale factor to the original perimeter to get the new perimeter.
$New\, perimeter = Original\, perimeter \times Scale\, factor$

STEP 4

Plug in the given values for the original perimeter and the scale factor to calculate the new perimeter.
$New\, perimeter = 16\, units \times 8$

STEP 5

Calculate the new perimeter.
$New\, perimeter = 16\, units \times 8 = 128\, units$
The perimeter of the figure after a dilation with a scale factor of 8 is 128 units, which corresponds to option (B).

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