To determine the new length of a picture when the width is reduced while maintaining the same aspect ratio, you need to set up a proportion based on the original dimensions and the new width.
The original dimensions of the picture are:
- Width: 10 inches
- Length: 12 inches
The new width of the picture is:
- Width: 9 inches
We need to find the new length, let's call it [tex]\( x \)[/tex].
Since the aspect ratio remains the same, we can set up the proportion of the original width to the original length and equate it to the proportion of the new width to the new length. This can be written as:
[tex]\[
\frac{\text{Original Width}}{\text{Original Length}} = \frac{\text{New Width}}{\text{New Length}}
\][/tex]
Substituting the known values:
[tex]\[
\frac{10}{12} = \frac{9}{x}
\][/tex]
To solve for [tex]\( x \)[/tex], we cross-multiply:
[tex]\[
10x = 12 \times 9
\][/tex]
Simplifying this, we get:
[tex]\[
10x = 108
\][/tex]
Now, divide both sides by 10 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{108}{10} = 10.8
\][/tex]
Therefore, the new length of the picture is 10.8 inches.
The correct proportion from the choices given is:
C. [tex]\(\frac{10}{12} = \frac{9}{x}\)[/tex]
So if you reduce the picture so that it is 9 inches wide, it will be 10.8 inches long.
