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Greetings.
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Today we have a question that deals with dimensional change.
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Here's our problem.
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Suppose a regular pentagon with a perimeter of 34 inches was dilated by a scale factor of 0 .25.
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So what we want to do first of all is we want to make sure that our scale factor is written as a fraction.
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So 0 .25 is the same as 1 over 4.
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We're asked to find the following.
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The pentagon's side length before dilation.
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So our pentagon had a perimeter when you added up all the sides of 34 inches.
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So a regular pentagon means that all the sides are equal.
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So to find one side length, when all the sides are equal, we just need to take the perimeter and divide it by the number of sides.
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Well, a pentagon has five sides, so we're going to divide that by five.
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And so that's going to be 6 .8.
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So each side was 6 .8 inches before we did a dilest.
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So now what's the new side length after dilation? so what we're going to do is we're going to set up a proportion with our scale factor equal to our side lengths written as a ratio.
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So we started with a side length of 6 .8 and then we multiplied that by 0 .25, which means it was going to get smaller.
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So we're going to match up the 6 .8 with the larger number of our scale factor...