# What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?

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When the length of a rectangle increases by 10% and its width decreases by 10%, the change in area can be calculated using the formula for the percentage change:

Percentage change = ((New value - Old value) / Old value) * 100

Let's denote:

- (L) as the original length of the rectangle,
- (W) as the original width of the rectangle,
- (A) as the original area of the rectangle.

After the changes:

- The new length (L_{\text{new}} = 1.10L) (increased by 10%),
- The new width (W_{\text{new}} = 0.90W) (decreased by 10%).

The new area (A_{\text{new}} = L_{\text{new}} \times W_{\text{new}} = (1.10L) \times (0.90W) = 0.99LW).

Using the percentage change formula:

[ \text{% Change} = \left( \frac{A_{\text{new}} - A}{A} \right) \times 100 ]

[ = \left( \frac{0.99LW - LW}{LW} \right) \times 100 ]

[ = \left( \frac{-0.01LW}{LW} \right) \times 100 ]

[ = -1% ]

Therefore, the percentage change in the area of the rectangle is a decrease of 1%.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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