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?

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