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 24 square centimeters 24 square centimeters 150 square centimeters 150 square centimeters 60 square centimeters 60 square centimeters 2.5 square centimeters

Answer 1

To find the area of the postcard, we need to know both the length and the width of the postcard. The problem specifies that the postcard has a length of 15 centimeters. However, we don't have the width directly given.

Since we're only given the length, let's assume the postcard maintains the same aspect ratio as the original photo.

The original photo measures 6 cm by 4 cm. The aspect ratio can be computed as follows:

\[
\text{Aspect Ratio} = \frac{\text{length}}{\text{width}} = \frac{6}{4} = \frac{3}{2}
\]

To find the width of the postcard while maintaining this aspect ratio with a length of 15 cm:

Let the width of the postcard be \( w \) centimeters:

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

Now we can cross-multiply to solve for \( w \):

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

Now that we have both dimensions of the postcard:
- Length = 15 cm
- Width = 10 cm

We can find the area of the postcard using the formula for the area of a rectangle (Area = length × width):

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

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