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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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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Answer 1 · 2018-03-04T01:47:08

I tried this:

Explanation:

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

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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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Explanation:

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