If the length of a rectangle is increased by 10% and the width of the rectangle is decreased by 10%, is the area changed? If so, does it increase or decrease and by what percent? Explain your answer.
the new area is
(1.1L)(0.9W) = 0.99 LW
so now you can tell how much the area has changed.
AWE MAN THANK YOU EVER SO MUCH STEVE TRULY APPRECIATE THE HELP
it decreased by 1 percent
To determine if the area of the rectangle changes, we need to calculate the before and after areas.
Let's assume the original length of the rectangle is L and the original width is W.
The area of the rectangle is given by A = L * W.
After increasing the length by 10%, the new length becomes L + 0.1L = 1.1L.
After decreasing the width by 10%, the new width becomes W - 0.1W = 0.9W.
The new area of the rectangle is A' = (1.1L) * (0.9W) = 0.99LW.
Now we can compare the original area (A) to the new area (A').
If A' is greater than A, then the area has increased. If A' is smaller than A, then the area has decreased.
Let's calculate the percentage change in area to determine if it has increased or decreased:
Change in area = (A' - A)
Percent change in area = [(Change in area) / A] * 100
If the percent change in area is positive, it means the area has increased. If it is negative, it means the area has decreased.
Substituting the values we calculated, the percent change in area is:
[(0.99LW - LW) / (LW)] * 100
When simplified, this becomes:
[(0.99 - 1) / 1] * 100 = -1%
The percent change in area is -1%. Therefore, the area has decreased by 1%.
So, if the length of a rectangle is increased by 10% and the width is decreased by 10%, the area decreases by 1%.