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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

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by AAPL » Mon Jun 28, 2021 8:50 am

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Magoosh

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

OA B
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Re: If the length and width of rectangle R are each increased by 1, the area of the new rectangle will be 72. If the len

by Brent@GMATPrepNow » Tue Jun 29, 2021 5:24 am
AAPL wrote: ↑
Mon Jun 28, 2021 8:50 am
 Magoosh

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

OA B
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
Brent Hanneson - Creator of GMATPrepNow.com
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