Question

suppose you are using a photocopier to reduce the size of a picture that is 8 inches wide and 11 inches long. if you reduce the picture to 7 inches wide, how long will it be?

Answer 1

To maintain the aspect ratio of the 8 inch by 11 inch picture when reducing the width to 7 inches, the new length would be 9.625 inches using a scale factor of 0.875.

Step-by-step explanation:

To answer the student's question about resizing an image using a photocopier, we need to maintain the aspect ratio of the original picture. The original dimensions are 8 inches by 11 inches. If the width is reduced to 7 inches and we want to find the new length while preserving the aspect ratio, we must first find the scale factor.

The scale factor is the ratio of the new width to the original width:
Scale factor = New width / Original width = 7 inches / 8 inches = 0.875.

Now, we apply this scale factor to the original length to get the new length:
New length = Scale factor × Original length = 0.875 × 11 inches = 9.625 inches.

So, if the picture is reduced to 7 inches wide, the length will be 9.625 inches to maintain the same proportion.

Answer 2

This is the concept of ratio and proportionality, to find the new length we shall use the formula;
(old length)/(old width)=(new length)/(old length)
This is because since the figures are similar, they have a constant factor that was used to dilate the pre-image into new image.
old length=11 inches
old width=8 inches
New length=x inches
new width= 7 inches;
Thus the new length will be:
11/8=x/7
multiplying both sides by 7/1 we get:
7/1*11/8=x/7*7/1
x=9 5/8