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:
$l=2w$
$l*w=A [tex](l-3)*w=A-12$

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.