Arectangle is 12 feet long and 5 feet wide. if the length of the rectangle is increased by 25% and the width is decreased by 20%, what is the change in the area of the rectangle?

The width is 6 and the length is 15. You multiply the length by 25% and then add that answer to the original length and then do the same for the width

Let 
L = old length of rectangle = 12 feet
W = old width of rectangle = 5 feet

Then area A of old rectangle is
A = L x W = (12 feet) x (5 feet) = 60 square feet

Now suppose
L' = new length of rectangle (increased by 25%)
W' = new width of rectangle (decreased by 20%)

Then
L' = L + 25% x L = 12 + 25% x 12 = 12 + 0.25 x 12 = 12 + 3 = 15 feet
and
W' = W - 20% x W = 5 - 20% x 5 = 5 - 0.20 x 5 = 5 - 1 = 4 feet

So, new area A' will be
A' = L' x W' = (15 feet) x (4 feet) = 60 square feet

The change in area is
A' - A = (60 square feet) - (60 square feet) = 0 square feet

This means there is no change in area.