To find the area of the postcard, we need to determine its dimensions. Since it is stated that the length of the postcard is 15 centimeters, we also need to find the width. Assuming the postcard retains the same aspect ratio as the original photo, we can calculate the width.
The original dimensions of the photo are:
- Length = 6 cm
- Width = 4 cm
The aspect ratio can be calculated as:
- Aspect ratio = Length / Width = 6 / 4 = 1.5
Let \( W \) be the width of the postcard, which we can find using the length of 15 cm while maintaining the same aspect ratio: \[ \frac{15}{W} = 1.5 \]
Cross-multiplying gives us: \[ 15 = 1.5W \]
Now, divide both sides by 1.5: \[ W = \frac{15}{1.5} = 10 \text{ cm} \]
Now we have the dimensions of the postcard:
- Length = 15 cm
- Width = 10 cm
To find the area \( A \) of the postcard, we use the formula for the area of a rectangle: \[ A = \text{Length} \times \text{Width} = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ square centimeters} \]
So, the area of the postcard is \( 150 \text{ square centimeters} \).
The correct response is: 150 square centimeters.