A picture measures 20 cm x 25 cm. The width of the matting and frame at the top and bottom is 5cm. What should be the dimensions of the frame so that the framed picture is similar to the picture alone
25/20 = 1.25
If it is the top that is 25 then
new side = 20+2*5 = 30
new top = 1.25*30 = 37.5
A 2 in frame surrounds a picture of 20in x 12in. Find the area of the frame.
Multiply then find out
Well, if the picture measures 20 cm x 25 cm, and you want the framed picture to be similar to the picture alone, then we need to maintain the same aspect ratio.
The aspect ratio can be calculated by dividing the width by the height. So, for the picture alone, the aspect ratio is 20/25 = 0.8.
Now, let's consider the width of the frame. Since there are two sides, the total width of the frame will be 2 times the width of the frame.
If the width of the frame is 5 cm, then the total width of the frame will be 2 * 5 cm = 10 cm.
To maintain the same aspect ratio, we need to increase both the width and height of the picture by the same factor. In this case, the factor can be calculated by dividing the new width (20 cm + 2 * 5 cm = 30 cm) by the original width (20 cm).
So, the factor is 30 cm / 20 cm = 1.5.
Now, we can multiply the original height (25 cm) by the factor to get the new height of the framed picture: 25 cm * 1.5 = 37.5 cm.
Therefore, the dimensions of the frame should be 10 cm x 12.5 cm.
To ensure that the framed picture is similar to the original picture, the aspect ratio of the two should be the same. The aspect ratio is the ratio of the width to the height of an object.
Given that the picture measures 20 cm x 25 cm, the aspect ratio can be calculated as 20/25 = 0.8.
To maintain the same aspect ratio for the framed picture, we need to find the dimensions of the frame that will keep the aspect ratio constant.
Let's assume that the width of the frame (top and bottom) is x cm.
The width of the framed picture will be the sum of the picture width and twice the frame width: 20 cm + 2x cm.
The height of the framed picture will be the sum of the picture height and twice the frame width: 25 cm + 2x cm.
The aspect ratio of the framed picture can be calculated by dividing the framed picture width by its height:
(20 cm + 2x cm) / (25 cm + 2x cm) = 0.8
To solve this equation, we can cross-multiply:
20 cm + 2x cm = 0.8 * (25 cm + 2x cm)
20 cm + 2x cm = 20 cm + 1.6x cm
Subtracting 20 cm from both sides gives:
2x cm = 1.6x cm
Now, subtracting 1.6x cm from both sides gives:
0.4x cm = 0
This equation implies that x = 0, which means there should be no width for the frame (top and bottom) to maintain the same aspect ratio between the framed picture and the original picture.
Therefore, the dimensions of the frame (top and bottom) should be 0 cm to ensure that the framed picture is similar to the original picture.