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Rectanlge

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by crackgmat007 » Sun Oct 11, 2009 12:40 pm
If the length and width of rectangle R are each increased by 1, the area of the new rectangle will be 72. If the length and width of rectangle R are each decreased by 1, the area of the new rectangle will be 35. What is the perimeter of rectangle R?

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by truplayer256 » Sun Oct 11, 2009 1:59 pm
(L+1)(W+1)=72-->LW+L+W+1=72 (A)

(L-1)(W-1)=35-->LW-L-W+1=35 (B)

Subtract equation B from A.

LW+L+W+1-LW+L+W-1=72-35

2L+2W=37

37 is our answer since the perimeter of rectangle R is equal to 2L+2W.
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by crackgmat007 » Sun Oct 11, 2009 2:35 pm
Is picking numbers not a good approach to attack this problem?
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by NikolayZ » Mon Oct 12, 2009 12:39 am
Hey Crackgmat!

I think that the most efficient way to solve this problem is the way Truplayer did. Because we don't have to find both sides' lengths, we just get the answer after the first step of 2 equations solution.
But i can be wrong, because i am the enemy of "picking numbers" strategy in Maths =)
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Re: Rectanlge

by Brent@GMATPrepNow » Sun Jul 25, 2021 6:30 am
crackgmat007 wrote: ↑
Sun Oct 11, 2009 12:40 pm
 If the length and width of rectangle R are each increased by 1, the area of the new rectangle will be 72. If the length and width of rectangle R are each decreased by 1, the area of the new rectangle will be 35. What is the perimeter of rectangle R?

24
37
48
50
51
Let L = the length of rectangle R
Let W = the width of rectangle R

If the length and width of rectangle R are each increased by 1, the area of the new rectangle will be 72.
We can write: (L + 1)(W + 1) = 72
Expand to get: LW + L + W + 1 = 72

If the length and width of rectangle R are each decreased by 1, the area of the new rectangle will be 35.
We can write: (L - 1)(W - 1) = 35
Expand to get: LW - L - W + 1 = 35

What is the perimeter of rectangle R?
The perimeter = L + W + L + W = 2L + 2W

So far we have:
LW + L + W + 1 = 72
LW - L - W + 1 = 35

When we subtract the bottom equation from the top equation we get: 2L + 2W = 37
Since the perimeter = 2L + 2W, we can see that the correct answer is B
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