To determine the area of the postcard, we need to calculate the area using the dimensions provided. The area \( A \) of a rectangle can be calculated using the formula:
\[ A = \text{length} \times \text{width} \]
Given that the length of the postcard is 15 centimeters, we first need to determine the width. The original photo dimensions are 6 cm by 4 cm, producing a ratio that can be used to resize the dimensions proportionally to the length of the postcard.
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Calculate the aspect ratio of the original photo: \[ \text{Aspect ratio} = \frac{6 \text{ cm}}{4 \text{ cm}} = \frac{3}{2} \]
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Now, to maintain this ratio when the length of the postcard is 15 cm, we can find the width using the aspect ratio. Let the width be \( w \) cm. Setting up the ratio: \[ \frac{15}{w} = \frac{3}{2} \]
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Cross-multiply to find \( w \): \[ 3w = 30 \implies w = 10 \text{ cm} \]
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Now we can calculate the area of the postcard: \[ A = \text{length} \times \text{width} = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ square centimeters} \]
Thus, the area of the postcard is 150 square centimeters.
The correct answer is: 150 square centimeters.