Final answer:
The overall percent change in the area of a rectangle, when the length increases by 20% and the width decreases by 20%, is a decrease of 4%.
Step-by-step explanation:
To calculate the overall percent change in the area of a rectangle when its dimensions change, we first consider the original length(L) and width(W). Imagine if L and W are both 100 units each for simplicity. If we increase the length by 20%, the new length becomes 120 units. If we decrease the width by 20%, the new width becomes 80 units.
Original area = L x W = 100 units x 100 units = 10000 square units.
New area = (L increased by 20%) x (W decreased by 20%) = 120 units x 80 units = 9600 square units.
The change in area = New area - Original area = 9600 square units - 10000 square units = -400 square units.
The percent change in area = (Change in area / Original area) x 100 = (-400 / 10000) x 100 = -4%.
So, the overall percent change in the area of the rectangle is a 4% decrease.