Question

5.) a polygon has a perimeter of 18 units. it is dilated with a scale factor of $\frac{3}{2}$. which of the following is the perimeter of its image? select one.
a.) 12 units b.) 24 units c.) 27 units d.) 30 units
6.) triangle abc is dilated to get triangle abc.
a.) which of these scale factors for the dilation would result in an image that was smaller than the original figure? circle all the apply.
a.) $\frac{3}{5}$ b.) $\frac{13}{17}$ c.) 1 d.) $\frac{4}{3}$
b.) explain your selection(s) in part (a).

Explanation:

Step1: Recall the property of dilation on perimeter

When a polygon is dilated with a scale factor \(k\), the perimeter of the image is \(k\) times the perimeter of the original polygon.

Step2: Calculate the perimeter of the dilated polygon

Given the original perimeter \(P = 18\) units and scale factor \(k=\frac{3}{2}\).
The perimeter of the image \(P_{image}=k\times P\)
Substitute \(k = \frac{3}{2}\) and \(P = 18\) into the formula:
\(P_{image}=\frac{3}{2}\times18\)

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Answer:

C. 27 units