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

150 square centimeters
150 square centimeters

24 square centimeters
24 square centimeters

2.5 square centimeters
2.5 square centimeters

60 square centimeters
60 square centimeters

Answer 1

To find the area of the postcard, we need to determine the dimensions of the postcard after resizing it.

The original photo measures 6 cm by 4 cm. The length of the postcard is given as 15 cm.

Since we want to maintain the aspect ratio while resizing, we can calculate the scaling factor. The original length of the photo is 6 cm, and we want the new length to be 15 cm.

The scaling factor is: $$\text{Scaling Factor}=\frac{\text{New Length}}{\text{Original Length}}=\frac{15\text{ cm}}{6\text{ cm}}=2.5.$$

We apply the scaling factor to the original width: $$\text{New Width}=\text{Original Width}\times \text{Scaling Factor}=4\text{ cm}\times 2.5=10\text{ cm}.$$

Now we have the dimensions of the postcard:

• Length = 15 cm
• Width = 10 cm

Next, we calculate the area of the postcard: $$\text{Area}=\text{Length}\times \text{Width}=15\text{ cm}\times 10\text{ cm}=150\text{ square centimeters}.$$

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