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)

Question

Responses

2.5 square centimeters
2.5 square centimeters

60 square centimeters
60 square centimeters

24 square centimeters
24 square centimeters

150 square centimeters

Answer 1

To find the area of the postcard, we can use the formula for the area of a rectangle, which is length multiplied by width.

The problem states that the length of the postcard is 15 centimeters. Since the original photo has a length-to-width ratio of 6 cm by 4 cm, we can find the width of the postcard by maintaining that same ratio.

First, let's find the ratio of the original dimensions: \[ \text{Ratio} = \frac{6 \text{ cm}}{4 \text{ cm}} = \frac{3}{2} \]

Now, if the length of the postcard is 15 cm, we can find the width using the ratio: Let the width be \( w \). Then we have: \[ \frac{15}{w} = \frac{3}{2} \]

Cross-multiply to solve for \( w \): \[ 3w = 30 \ w = 10 \text{ cm} \]

Now that we have both the length (15 cm) and the width (10 cm) of the postcard, we can calculate the 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.