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 to the size of a postcard with a length of 15 centimeters. What will be the area of the postcard?
To solve this problem, we need to use proportions. We know that the length of the original print is 6 centimeters and the length of the postcard is 15 centimeters. We can set up a proportion:
6 cm / 4 cm = 15 cm / x
where x is the width of the postcard. To solve for x, we can cross-multiply and simplify:
6 cm * x = 4 cm * 15 cm
6x = 60 cm
x = 10 cm
So the width of the postcard is 10 centimeters. The area of the postcard is:
15 cm * 10 cm = 150 square centimeters.
Therefore, the area of the postcard is 150 square centimeters.
To solve this problem, we need to find the area of the postcard after resizing the photo.
First, let's find the width of the postcard. We know that the width of the photo is 6 centimeters. To resize it, we need to find the scaling factor, which is the ratio of the new width to the original width. In this case, the new width is 15 centimeters, and the original width is 6 centimeters.
Scaling Factor = New Width / Original Width
Scaling Factor = 15 cm / 6 cm = 2.5
Next, we need to find the new height of the photo by multiplying the scaling factor with the original height. The original height of the photo is 4 centimeters.
New Height = Scaling Factor * Original Height
New Height = 2.5 * 4 cm = 10 cm
Now, we have the new dimensions of the photo, which are 2.5 times larger than the original. To find the area of the postcard, we multiply the new width with the new height.
Area of Postcard = New Width * New Height
Area of Postcard = 15 cm * 10 cm = 150 square centimeters
So, the area of the postcard will be 150 square centimeters.
To find the area of the postcard, we first need to determine the width of the postcard since we already have the length.
Given that Natalia wants the width of the postcard to be the same ratio as the original print, which is 6 centimeters by 4 centimeters, we can set up the following proportion:
Original width / Original length = Postcard width / Postcard length
6 cm / 4 cm = Postcard width / 15 cm
To solve for the postcard width, we cross-multiply:
6 cm * 15 cm = 4 cm * Postcard width
90 cm^2 = 4 cm * Postcard width
Now, divide both sides by 4 cm:
90 cm^2 / 4 cm = Postcard width
22.5 cm = Postcard width
So, the width of the postcard is 22.5 centimeters.
To find the area of the postcard, we multiply the width by the length:
Area = Width * Length
Area = 22.5 cm * 15 cm
Area = 337.5 cm^2
Therefore, the area of the postcard will be 337.5 square centimeters.