I am having trouble with this question. I do not know where to begin. I am in Trig now and we are doing review but I forgot everything that I learned in Geometry. I want to understand how to do this problem.
"a picture measures 20 cm by 25 cm. the width of the matting and frame at top and bottom is 5 cm. how wide should the matting and frame be at the sides so that the framed picture is similar to the picture alone"
Let's assume that you are hanging the picture vertically, that is, the width is 20 and the length vertically is 25.
so you want to maintain the ratio of height : width
right now, height : width = 25 : 20 = 5 : 4
new width = 20+10 = 30
new height = x
x/30 = 5/4
4x = 150
x = 37.5
increase in height = 37.5-25 = 12.5 cm
or 6.25 cm on each side
Notice I added the 5 cm to each end of the 20 cm side.
If otherwise, add the 5 cm each to the 25 cm side
To solve this problem, we need to understand similarity and the concept of corresponding sides. Similar figures have the same shape but may have different sizes. In this case, we want to find the width of the matting and frame at the sides so that the framed picture is similar to the picture alone.
First, let's identify the corresponding sides of the framed picture and the picture alone:
- The width of the framed picture is 20 cm - 2 * 5 cm = 10 cm. This corresponds to the width of the picture alone.
- The height of the framed picture is 25 cm - 2 * 5 cm = 15 cm. This corresponds to the height of the picture alone.
Since the framed picture and the picture alone are similar, their corresponding sides must have the same ratio.
To find the width of the matting and frame at the sides, we need to set up a proportion between the widths:
(Width of matting and frame at sides) / (Width of matting and frame at top/bottom) = (Width of picture alone) / (Width of framed picture)
Let's substitute the known values into this equation:
(Width of matting and frame at sides) / 5 cm = 10 cm / 15 cm
Now, we solve for the width of the matting and frame at the sides:
(Width of matting and frame at sides) = (5 cm) * (10 cm / 15 cm)
Simplifying, we have:
(Width of matting and frame at sides) = 3.33 cm
Therefore, the width of the matting and frame at the sides should be approximately 3.33 cm to ensure that the framed picture is similar to the picture alone.