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

To ensure that the framed picture is similar to the picture alone, we need to maintain the same aspect ratio between the width and height. In this case, the aspect ratio is given as 20 cm : 25 cm or 4 : 5.

Let's determine the dimensions of the frame.

1. Calculate the width of the framed picture:
The width of the picture (without frame) is 20 cm. Since the frame adds 5 cm on each side, the total width of the framed picture is:
Width of the framed picture = width of the picture + (2 × width of the frame) = 20 cm + (2 × 5 cm) = 20 cm + 10 cm = 30 cm.

2. Calculate the height of the framed picture:
The height of the picture (without frame) is 25 cm. Since the frame adds 5 cm on each side at the top and bottom, the total height of the framed picture is:
Height of the framed picture = height of the picture + (2 × height of the frame) = 25 cm + (2 × 5 cm) = 25 cm + 10 cm = 35 cm.

Therefore, the dimensions of the frame should be 30 cm x 35 cm to ensure that the framed picture is similar to the picture alone.

To find the dimensions of the frame, we need to ensure that the ratio of the width and height of the frame is the same as the ratio of the width and height of the picture.

Given that the picture measures 20 cm x 25 cm, the ratio of width to height is 20:25, which can be simplified to 4:5.

Now, let's calculate the width and height of the frame using this ratio.

Since the width of the frame on both the top and bottom is 5 cm, the total width of the frame will be 5 cm + 20 cm + 5 cm = 30 cm.

To maintain the ratio of 4:5, we can consider the width as 4x and the height as 5x, where x is a constant.

Therefore, the width of the framed picture will be 30 cm, which is equal to 4x.

Solving this equation, we find x = 7.5 cm.

Now, we can calculate the height as 5x = 5 * 7.5 cm = 37.5 cm.

So, the dimensions of the frame should be 30 cm x 37.5 cm, to ensure that the framed picture is similar to the picture alone.

Assuming that the sides also have 5cm of matting, (20+10)cm by (25+10)cm.