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

Mar 4, 2018

I tried this:

#### Explanation:

Let us call the length $l$ and width $w$; we get for the area $A$:
$A = l \cdot w$
let us change the two to get:
$A ' = \left(l + 0.1 l\right) \cdot \left(w - 0.1 w\right)$
rearrange:
$A ' = l w \cancel{- 0.1 l w} + \cancel{0.1 l w} - 0.01 l w$
$A ' = 0.99 l w$
but $A = l w$ so substituting:
$A ' = 0.99 A$
so the new area is 99% of $A$.
For example;
imagine a rectangle where:
$l = 10$ and $w = 5$
Area$= 10 \cdot 5 = 50$
Now we increase the length and decrease the width:
$l = 10 + 0.1 \cdot 10 = 11$
$w = 5 + 0.1 \cdot 5 = 4.5$
Area'$= 11 \cdot 4.5 = 49.5$
that represents 99% of $50$.