9. Given a scale factor of 3, find the coordinates for the dilation of a triangle with vertices at
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Answer:
<u>24 meters</u> is the width of the original rectangle.
Step-by-step explanation:
Given:
Bobby knows that the perimeter of the original rectangle is 120 meters. He also knows that the perimeter of the reduced rectangle is 30 meters and the reduced rectangle has a length of 9 meters.
Now, to get the width of original rectangle.
The reduced rectangle's perimeter = 30 meters.
The reduced rectangle's length = 9 meters.
Now, we find the width of reduced rectangle by using formula:
Let the width of reduced rectangle be
<em>Subtracting both sides by 18 we get:</em>
<em /><em />
<em>Dividing both sides by 2 we get:</em>
The width of reduced rectangle = 6 meters.
Now, to get the width of original rectangle:
Let the width of original rectangle be
<em>As given, the perimeter of the original rectangle = 120 meters.</em>
<em>And, the perimeter of reduced rectangle is 30 meters and its width is 6 meters.</em>
<em>So, 30 is equivalent to 6.</em>
<em>Thus, 120 is equivalent to </em><em />
Now, to get the width using cross multiplication method:
<em>By cross multiplying we get:</em>
<em /><em />
<em>Dividing both sides by 30 we get:</em>
<em /><em />
<em>The width of original rectangle = 24 meters.</em>
Therefore, 24 meters is the width of the original rectangle.