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The length of side XY is 20.25 inches.
In the image, pentagon UVWXY is similar to pentagon JKLMN, and we are asked to find the length of side XY. We can do this by setting up a proportion between the corresponding sides of the two similar pentagons.
From the image, we can see that:
Side MN has a length of 27 inches.
Side XY has a length of x inches (which we are trying to find).
The scale factor between the two pentagons is 30/40 = 3/4.
Setting up the proportion, we get:
XY / MN = 3/4
Substituting the known values, we get:
x / 27 = 3/4
Solving for x, we get:
x = (3/4) × 27
x = 20.25 inches
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