Question

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

Answer 1

I tried this:

Explanation:

Let us call the length `l` and width `w`; we get for the area `A`:
`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`.