Question

Solve the following problem: Natalia prints a photo of a covered bridge. The print measures 6 centimeters by 4 centimeters. She wants to resize the photo into the size of a postcard with a length of 15 centimeters. What will be the area of the postcard?(1 point)
Responses

60 square centimeters
60 square centimeters

24 square centimeters
24 square centimeters

150 square centimeters
150 square centimeters

2.5 square centimeters

Answer 1

To find the area of the postcard, we need to know its width in addition to its length. The length of the postcard is given as 15 centimeters. However, since we don't have the width, we can reasonably assume that the postcard maintains the same aspect ratio as the original photo (6 cm by 4 cm).

First, we can calculate the aspect ratio of the original photo:

- The width of the original photo is 4 cm, and the length is 6 cm.
- The aspect ratio (width to length) is \( \frac{4}{6} = \frac{2}{3} \).

If we let the width of the new postcard be \( w \), then using the aspect ratio we have:

\[
\frac{w}{15} = \frac{2}{3}.
\]

To find \( w \), we can cross-multiply:

\[
3w = 2 \times 15.
\]
\[
3w = 30.
\]
\[
w = \frac{30}{3} = 10 \text{ cm}.
\]

Now we can calculate the area of the postcard using the formula for area:

\[
\text{Area} = \text{length} \times \text{width} = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ square centimeters}.
\]

Therefore, the area of the postcard is:

**150 square centimeters.**