Question

The length of a certain rectangle is twice its width. if the lenth is decreased by 3 cm, the area of the resultign recatangle is 12 sq cm less than the area of the original rectangle. find the original dimensions

Answer 1

Here's what we know:

`l=2w`

`image`

Now let's substitute in what we know from the first equation into the third equation:

`(2w-3)*w=A-12`

`2w^(2)-3w=A-12`

`2w^(2)-3w+12=A=l*w=2w*w=2w^(2)`

`-3w+12=0`

`-3w=-12`

`w=4`

Since we know the relationship between length and width:

`l=2w=2*4=8`

So l=8, w=4.