To find the area of the rectangle after dilation, we start with the original area.
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Calculate the original area of the rectangle: \[ \text{Original area} = \text{length} \times \text{width} = 5 \text{ units} \times 3 \text{ units} = 15 \text{ square units} \]
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A dilation by a scale factor of \(k\) multiplies both the length and width by that scale factor. In this case, the scale factor is 5.
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New length: \[ \text{New length} = 5 \text{ units} \times 5 = 25 \text{ units} \]
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New width: \[ \text{New width} = 3 \text{ units} \times 5 = 15 \text{ units} \]
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Now, calculate the new area: \[ \text{New area} = \text{New length} \times \text{New width} = 25 \text{ units} \times 15 \text{ units} = 375 \text{ square units} \]
Therefore, the new area of the rectangle after dilation is \(375\) square units.