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.

since a=lw, your new area is

(1.1l)(0.9w) = 0.99 lw

So the area has decreased by 1%

Well, you could say: since every square is a rectangle 'because it is a quadrilateral with all four angles right angles,' therefore the area didn't change.

To determine whether the area of the rectangle changes when the length is increased by 10% and the width is decreased by 10%, we can follow these steps:

Step 1: Let's assume the initial length of the rectangle is L and the initial width is W.
Step 2: Calculate the initial area of the rectangle using the formula: Area = Length * Width, so Initial Area = L * W.
Step 3: Increase the length by 10%: New Length = L + 0.1L = 1.1L.
Step 4: Decrease the width by 10%: New Width = W - 0.1W = 0.9W.
Step 5: Calculate the new area of the rectangle using the formula: New Area = New Length * New Width = 1.1L * 0.9W.

Now, let's compare the initial area and the new area to determine whether there has been any change:

If New Area > Initial Area, then the area has increased.
If New Area < Initial Area, then the area has decreased.

Let's calculate the new area:

New Area = 1.1L * 0.9W = 0.99LW

Comparing the initial area (LW) and the new area (0.99LW), we can see that the new area is slightly smaller than the initial area. Therefore, the area of the rectangle has decreased.

To calculate the change in the area, we can use the following formula:

Change in Area = ((New Area - Initial Area) / Initial Area) * 100

Change in Area = ((0.99LW - LW) / LW) * 100 = ((-0.01LW) / LW) * 100 = -1%

Therefore, the area of the rectangle decreases by 1% when the length is increased by 10% and the width is decreased by 10%.