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

150 square centimeters
150 square centimeters

60 square centimeters
60 square centimeters

2.5 square centimeters
2.5 square centimeters

24 square centimeters

1 answer

To find the area of the postcard, we need to determine its dimensions. Since it is stated that the length of the postcard is 15 centimeters, we also need to find the width. Assuming the postcard retains the same aspect ratio as the original photo, we can calculate the width.

The original dimensions of the photo are:

  • Length = 6 cm
  • Width = 4 cm

The aspect ratio can be calculated as:

  • Aspect ratio = Length / Width = 6 / 4 = 1.5

Let \( W \) be the width of the postcard, which we can find using the length of 15 cm while maintaining the same aspect ratio: \[ \frac{15}{W} = 1.5 \]

Cross-multiplying gives us: \[ 15 = 1.5W \]

Now, divide both sides by 1.5: \[ W = \frac{15}{1.5} = 10 \text{ cm} \]

Now we have the dimensions of the postcard:

  • Length = 15 cm
  • Width = 10 cm

To find the area \( A \) of the postcard, we use the formula for the area of a rectangle: \[ A = \text{Length} \times \text{Width} = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ square centimeters} \]

So, the area of the postcard is \( 150 \text{ square centimeters} \).

The correct response is: 150 square centimeters.