To find the area of the postcard, we need to know its dimensions. Given that the length of the postcard is 15 centimeters, we first need to find the width.
The original photo measures 6 cm by 4 cm, which gives it an area of: \[ \text{Area of photo} = 6 , \text{cm} \times 4 , \text{cm} = 24 , \text{cm}^2 \]
If Natalia resizes the photo to a postcard size with a length of 15 cm, assuming she maintains the same aspect ratio (width to length ratio), we will find the width of the postcard.
The aspect ratio of the original photo is: \[ \text{Aspect ratio} = \frac{4 , \text{cm}}{6 , \text{cm}} = \frac{2}{3} \]
Let's denote the width of the postcard as \( w \). Since she wants the length to be 15 cm, we can maintain the same aspect ratio: \[ \frac{w}{15 , \text{cm}} = \frac{2}{3} \]
Cross-multiplying gives: \[ 3w = 2 \times 15 \] \[ 3w = 30 \] \[ w = \frac{30}{3} = 10 , \text{cm} \]
Now we have the dimensions of the postcard: 15 cm long and 10 cm wide.
Next, we calculate the area of the postcard: \[ \text{Area of postcard} = \text{length} \times \text{width} = 15 , \text{cm} \times 10 , \text{cm} = 150 , \text{cm}^2 \]
The area of the postcard is 150 square centimeters.
Thus, the correct response is: 150 square centimeters.