Finding Original Dimensions

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wew

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a rectangele is 8 cm longer than it is wide. If its length and width are both increased by 2cm, its are is decreased by 108cm. find its original dimensions.

please help me!!!
 
Are you sure, SURE, S-U-R-E that you copied the problem statement correctly? Perhaps the Area INcreased? I think you will not like the answer to the problem as stated.
 
Wow i copied it totally wrong.

A rectangle is twice as long as it is wide. If its length and width are both decreased by 4cm, its area is decreased by 164cm squared. Find its original dimensions.




and




A rectangle is 8cm longer than it is wide. If its length and width are both increased by 2cm, its area is decreased by 108cm squared . Find its originial dimensions.
 
wew said:
1) A rectangle is twice as long as it is wide. If its length and width are both decreased by 4cm, its area is decreased by 164cm squared. Find its original dimensions.
Click to expand...
We'll just ignore that other one. I get Width = -32 cm, as stated. Not pretty.

Read the problem statement. What are we talking about? Rectangles. First, search your brain for anything you know about rectangles.

1) Length
2) Width
3) Area = Length * Width
4) Perimeter = 2*Length + 2*Width
5) Four Right angles
6) Two pair of congruent sides.
6) Special Parallelogram - one with right angles.
8) Maybe the Assyrians used to worship them.
9) Houses and building often are constructed with them in the design.
10) They don't look much like cows.

Really, just ANYTHING you know. You may need it. Switch on your brain and leave it on, just in case you miss something on the first pass.

Read the problem statement again and try to judge what you might need.

I think we'll need Area = Length * Width

What is the length? We don't know, so call it something. How about 'L'?
What is the width? We don't know, so call it something. How about 'W'?

What about them?

"A rectangle is twice as long as it is wide."

Oh, then L = 2*W

"If its length and width are both decreased by 4cm"

OK, that's (L-4) and (W-4), so what?

"its area is decreased by 164cm squared"

It's NEW AREA is (L-4)*(W-4).

OK, but that's 164 cm^2 less than what? The OLD AREA. What's that?

It's OLD AREA is L*W

Now we have (L-4)*(W-4) = L*W - 164

Now what? You tell me.
 
well im using n and this is wha ti did i said n=width and 2n=length, so is it?
(n-4)(2n-4)=n(2n)-164?
 
wew said:
Wow i copied it totally wrong.
"A rectangle is twice as long as it is wide. If its length and width are both decreased by 4cm, its area is decreased by 164cm squared. Find its original dimensions."

Well, let's see where you're at:
let w = width
what then is the length?

and what is the width and length of the decreased rectangle?

What is the formula for the area of a rectangle?



"A rectangle is 8cm longer than it is wide. If its length and width are both increased by 2cm, its area is decreased by 108cm squared . Find its originial dimensions."

C'MON! TK already told you the area CANNOT decrease if you're
increasing the dimensions...make that "increased", OK?
let w = width
then what is the length?

what are the increased width and length?
Click to expand...

EDIT: Whoops...sorry TK: didn't mean to interfere...
 
Not bad, except that the '25' should be a '2n', shouldn't it?
Edit: Ah, I see you changed it already. Good catch.

That's where I was going next. We can't do much with two variables and only one equation, wo we have to get rid of a variable.

(L-4)*(W-4) = L*W - 164

Since we know L = 2*W, we have:

(2*W-4)*(W-4) = (2*W)*W - 164

Since I used different names, it may not look exactly the same, but it really is. OK, what's next?
 
Denis said:
EDIT: Whoops...sorry TK: didn't mean to interfere...
Click to expand...
No worries.

wew: You have to have a little patience with us. It's been a REALLY SLOW math day and we're all a little punchy. :x
 
wew said:
(n-4)(2n-4)=n(2n)-164?
Click to expand...
Your leaning the right direction. Now just jump in. Expand and simplify.

(n-4)(2n-4)=n(2n)-164

I'll do the expand. You do the simplify.

2*n<sup>2</sup> - 12*n + 16 = 2*n<sup>2</sup> - 164

Do you see where all that came from? Just FOIL and stuff...
 
I know, sorry. Its just that my tutor she gave me two pages of these problems that i do not know how to do so i have 20 problems of complete confusion to me that i have to finish. And i really have no idea how to. And if i dont finish my mom gets seriously angry with me and i get in lots of trouble.

Sorry.
 
That's just multiplication. 2n = 2*n

Thanks for asking. Some folks choose to remain confused by new notation.
 
wew said:
Um. n(2n)=2n^?
Click to expand...

n(2n) = 2n^2

n(2n) means n times (2n); and 2n means 2 times n;
so you have n times 2 times n;
n times n = n squared which is shown as n^2

so we're left with 2 times n^2 = 2n^2

LISTEN wew:
if your problem was not knowing which symbols to use
(like * for multiplication and ^ for "to the power")
then you shouldn't worry too much: once you know, YOU KNOW!
BUT, BUT, if your problem is not knowing basic stuff like the area
of a rectangle, then you're in trouble and need to go back to basics;
...else Mom will REALLY be mad!
 
TKH gave you
2*n2 - 12*n + 16 = 2*n2 - 164
You gathered like terms.
2*n^2 - 2*n^2 + 16 + 164 - 12*n = 0
12*n = 180
n=15 is correct.
 
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