To find the area of the postcard, we first need to determine the dimensions of the postcard using its length. The dimensions of the original print (6 cm by 4 cm) need to be scaled to a length of 15 cm.
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Calculate the scaling factor for the length: \[ \text{Scaling factor} = \frac{\text{New length}}{\text{Original length}} = \frac{15 , \text{cm}}{6 , \text{cm}} = 2.5 \]
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Use this scaling factor to find the new height: \[ \text{New height} = \text{Original height} \times \text{Scaling factor} = 4 , \text{cm} \times 2.5 = 10 , \text{cm} \]
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Now, the dimensions of the postcard are 15 cm (length) and 10 cm (height).
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Calculate the area of the postcard: \[ \text{Area} = \text{Length} \times \text{Height} = 15 , \text{cm} \times 10 , \text{cm} = 150 , \text{cm}^2 \]
Therefore, the area of the postcard will be 150 square centimeters.