The area of a rectangle is the product of its dimensions, that is:
Area = length * width
Then, if we call A the area, L the length, and W the width, the original area can be written as:
A = L * W
and the new area A' (after the increase of the length and the decrease of the width) would be:
A' = (1.2L) * (0.8W)
Notice that we wrote the 20% increase as 1.2 times the original length. That's so because, when L increases 20%, it becomes:
L' = L + 20% L
= (1 + 20%) L
= (1 + 0.2)L
= 1.2L
And, when W decreases 20%, it becomes:
W' = W - 20% W
= (1 - 20%) W
= (1 - 0.2) W
= 0.8 W
Now, proceeding to find the effect on the area, we find:
A' = (1.2L) * (0.8W)
= (1.2 * 0.8) * L * W
= 0.96 * (L * W)
= 0.96 * A
= (1 - 0.04) * A
= (1 - 4%) * A
= A - 4% A
Therefore, the effect on the area of the rectangle is the following:
• the ,area ,is ,decreased by 4%,.