To find the area of the postcard, we need to calculate the area using the dimensions provided.
Given that the length of the postcard is 15 centimeters, we also need to find the corresponding width. The aspect ratio of the original photo (6 cm by 4 cm) is 6:4 or 3:2.
To maintain this ratio when resizing, we can express the width \( w \) in terms of the length \( l \): \[ \frac{l}{w} = \frac{3}{2} \quad \Rightarrow \quad w = \frac{2}{3}l \]
Using the length of the postcard: \[ w = \frac{2}{3} \times 15 = 10 \text{ centimeters} \]
Now we have the dimensions of the postcard: 15 centimeters long and 10 centimeters wide.
Next, we can calculate the area \( A \): \[ A = \text{length} \times \text{width} = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ square centimeters} \]
Thus, the area of the postcard is 150 square centimeters.
The correct response is: 150 square centimeters.