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
Here's what we know: [tex]l=2w[/tex] [tex]l*w=A [tex](l-3)*w=A-12[/tex]
Now let's substitute in what we know from the first equation into the third equation: [tex](2w-3)*w=A-12[/tex] [tex]2w^{2}-3w=A-12[/tex] [tex]2w^{2}-3w+12=A=l*w=2w*w=2w^{2}[/tex] [tex]-3w+12=0[/tex] [tex]-3w=-12[/tex] [tex]w=4[/tex]
Since we know the relationship between length and width: [tex]l=2w=2*4=8[/tex]
