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Math Expert V
Joined: 02 Sep 2009
Posts: 58427
If the length and width of rectangle R are each increased by 1, the ar  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 81% (02:32) correct 19% (02:53) wrong based on 37 sessions

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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?

A. 34
B. 37
C. 48
D. 50
E. 51

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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If the length and width of rectangle R are each increased by 1, the ar  [#permalink]

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1
Area of R = (L+1)(W+1) = 72
WL+l+W = 71...........(1)
New area = (L-1)(W-1) = 35
WL-L-W = 34.............(2)
(1)-(2) = 2L+2W = 37 = Perimeter

B is the answer.
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Joined: 18 Aug 2017
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Re: If the length and width of rectangle R are each increased by 1, the ar  [#permalink]

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Bunuel wrote:
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?

A. 34
B. 37
C. 48
D. 50
E. 51

(x+1)*(y+1)=72
(x-1)*(y-1)=35
solve and subtract eqn
-2(x+y)= 37
which is perimeter

IMO B
Target Test Prep Representative D
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Joined: 14 Oct 2015
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Re: If the length and width of rectangle R are each increased by 1, the ar  [#permalink]

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Bunuel wrote:
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?

A. 34
B. 37
C. 48
D. 50
E. 51

We can create the equations:

(L + 1)(W + 1) = 72

LW + L + W + 1 = 72

LW + L + W = 71 → (Eq. 1)

and

(L - 1)(W - 1) = 35

LW - L - W + 1 = 35

LW - L - W = 34 → (Eq. 2)

Subtracting Eq. 2 from Eq. 1, we have:

2L + 2W = 37

Since 2L + 2W is the perimeter of rectangle R, the perimeter of rectangle R is 37.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If the length and width of rectangle R are each increased by 1, the ar   [#permalink] 10 Feb 2019, 08:39
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If the length and width of rectangle R are each increased by 1, the ar

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