Question
Solve the following problem Natalie print a photo of a covered bridge. The print measures 6 cm x 4 cm. She wants to resize the photo into the size of a postcard with a length of 15 cm. What will be the area of the postcard?
24 cm²
2.5 cm²
150 cm²
or 60 cm²
24 cm²
2.5 cm²
150 cm²
or 60 cm²
Answers
GPT-4o mini
To find the area of the postcard, we need to know both its length and width. Given that the postcard has a length of 15 cm, let's first calculate the width.
Since the original photo measures 6 cm x 4 cm, we can determine the aspect ratio of the original photo:
- Aspect ratio: 6 cm / 4 cm = 1.5
When resizing the length of the photo to 15 cm, we can maintain the same aspect ratio. Thus, we can find the new width (W) using the following equation:
\[
\text{Aspect ratio} = \frac{\text{Length}}{\text{Width}} \Rightarrow 1.5 = \frac{15 \text{ cm}}{W}
\]
Now, we can solve for \( W \) (the new width):
\[
W = \frac{15 \text{ cm}}{1.5} = 10 \text{ cm}
\]
Now that we have the dimensions of the postcard (15 cm x 10 cm), we can find its area (A) using the formula for the area of a rectangle:
\[
A = \text{length} \times \text{width} = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ cm}²
\]
So, the area of the postcard is **150 cm²**.
Since the original photo measures 6 cm x 4 cm, we can determine the aspect ratio of the original photo:
- Aspect ratio: 6 cm / 4 cm = 1.5
When resizing the length of the photo to 15 cm, we can maintain the same aspect ratio. Thus, we can find the new width (W) using the following equation:
\[
\text{Aspect ratio} = \frac{\text{Length}}{\text{Width}} \Rightarrow 1.5 = \frac{15 \text{ cm}}{W}
\]
Now, we can solve for \( W \) (the new width):
\[
W = \frac{15 \text{ cm}}{1.5} = 10 \text{ cm}
\]
Now that we have the dimensions of the postcard (15 cm x 10 cm), we can find its area (A) using the formula for the area of a rectangle:
\[
A = \text{length} \times \text{width} = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ cm}²
\]
So, the area of the postcard is **150 cm²**.