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

2.5 square centimeters
2.5 square centimeters

24 square centimeters
24 square centimeters

150 square centimeters
150 square centimeters

60 square centimeters

Answer 1

To determine the area of the postcard, we need to calculate the area using the dimensions provided. The area \( A \) of a rectangle can be calculated using the formula:

\[
A = \text{length} \times \text{width}
\]

Given that the length of the postcard is 15 centimeters, we first need to determine the width. The original photo dimensions are 6 cm by 4 cm, producing a ratio that can be used to resize the dimensions proportionally to the length of the postcard.

1. Calculate the aspect ratio of the original photo:
\[
\text{Aspect ratio} = \frac{6 \text{ cm}}{4 \text{ cm}} = \frac{3}{2}
\]

2. Now, to maintain this ratio when the length of the postcard is 15 cm, we can find the width using the aspect ratio.
Let the width be \( w \) cm. Setting up the ratio:
\[
\frac{15}{w} = \frac{3}{2}
\]

3. Cross-multiply to find \( w \):
\[
3w = 30 \implies w = 10 \text{ cm}
\]

4. Now we can calculate the area of the postcard:
\[
A = \text{length} \times \text{width} = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ square centimeters}
\]

Thus, the area of the postcard is **150 square centimeters**.

The correct answer is: **150 square centimeters**.