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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 :

alphabetsam
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]

So l=8, w=4.

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