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A rectangular picture is to be framed. If the width of the

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A rectangular picture is to be framed. If the width of the [#permalink] New post 28 Jul 2007, 08:56
6. A rectangular picture is to be framed. If the width of the frame is 1, the area of the framed picture would be m; is the width of the frame is 2, the area of the framed picture would be m+52. What is the perimeter of the un-framed picture?
A.36
B.40
C.54
D.60
E.72
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Re: Rectangular [#permalink] New post 28 Jul 2007, 10:48
jet1445 wrote:
6. A rectangular picture is to be framed. If the width of the frame is 1, the area of the framed picture would be m; is the width of the frame is 2, the area of the framed picture would be m+52. What is the perimeter of the un-framed picture?
A.36
B.40
C.54
D.60
E.72


I am getting B.

length of unframed picture = l
width of unframed picture = b

when width of frame is 1.
Area of framed pic = (l+2)(b+2)
Therefore, 2l + 2b + lb + 4 = m...[I]

when width of frame is 2.
Area of framed pic = (l+4)(b+4)
Therefore, 4l + 4b + lb + 16 = m+52...[II]

Subtract [I] from [II].

2l + 2b + 12 = 52
or, 2*(l+b) = 40 = perimeter of unframed pic
Re: Rectangular   [#permalink] 28 Jul 2007, 10:48
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