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# A rectangular photograph is surrounded by a border that is 1

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Manager
Joined: 10 Oct 2005
Posts: 113
Location: Hollywood
A rectangular photograph is surrounded by a border that is 1 [#permalink]

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30 Sep 2006, 08:41
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A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M+52) square inches. What is the perimeter of the photograph, in inches?
A- 34
B- 36
C- 38
D- 40
E- 42
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Senior Manager
Joined: 11 May 2006
Posts: 258

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30 Sep 2006, 09:08
let the sides of border be x and y

so xy = M

after increasing the width,
then (x+2)(y+2) = M+52
=> M + 2x + 2y + 4 = M + 52
=> x + y = 24

now sides of photograph are (x-2) and (y-2) because of 1 inch border
so perimeter of photograph = 2[ x -2 + y - 2] = 2 [ 24-4] = 40

hence D
Director
Joined: 06 Sep 2006
Posts: 736
Re: PS - Nice geometry word problems [#permalink]

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30 Sep 2006, 14:17
TOUGH GUY wrote:
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M+52) square inches. What is the perimeter of the photograph, in inches?
A- 34
B- 36
C- 38
D- 40
E- 42

If X and Y are the length and width of the photograph respectively (excluding the border) then

(X + 2)(Y + 2) = M ( since border is 1 inch on each side)
XY + 2X + 2Y + 4 = M ---> A

Also,
(X + 4) (Y + 4) = M + 52 (if border is 2 inch wide on each side)
XY + 4X + 4Y + 16 = 52 ---> B

Subtract A from B

2X + 2Y + 12 = 52
2X + 2Y = 40
2X + 2Y = Perimeter of photograph

So, D.
SVP
Joined: 05 Jul 2006
Posts: 1747

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30 Sep 2006, 14:41
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M+52) square inches. What is the perimeter of the photograph, in inches?
A- 34 B- 36 C- 38 D- 40 E- 42

let the sides of the photograph be L,W

AREA OF TOTAL = (L+2)(W+2)=M...............ONE

IF CONDITION ....M+52 = (L+4)(W+4)......TWO

FROM ONE AND TWO

LW+2L+2W+56 = LW+4L+4W+16

2L+2W = 40......MY ANSWER IS D
30 Sep 2006, 14:41
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# A rectangular photograph is surrounded by a border that is 1

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