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

Answer 1

To find the area of the postcard, we need to know both its length and width. The length of the postcard is given as 15 centimeters.

To maintain the same aspect ratio as the original photo (6 cm by 4 cm), we can calculate the width of the postcard. The aspect ratio is 6:4, which can be simplified to 3:2.

1. Let's denote the width of the postcard as \( W \).
2. The aspect ratio tells us that \( \frac{Width}{Length} = \frac{2}{3} \).

Setting up the proportion based on the length of the postcard:

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

Now, cross-multiplying to solve for \( W \):

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

Now we have the dimensions of the postcard: 15 cm (length) and 10 cm (width).

Next, we can calculate the area of the postcard:

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

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

Thus, the correct response is 150 square centimeters.