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A square picture frame has an outer perimeter of 36 inches and is 1 in

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Math Expert
Joined: 02 Sep 2009
Posts: 61385
A square picture frame has an outer perimeter of 36 inches and is 1 in  [#permalink]

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04 Oct 2017, 10:11
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25% (medium)

Question Stats:

85% (00:52) correct 15% (00:47) wrong based on 24 sessions

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A square picture frame has an outer perimeter of 36 inches and is 1 inch wide on all sides. What is the inner perimeter of the frame, in inches?

(A) 27
(B) 27 1/2
(C) 28
(D) 31 1/2
(E) 32

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Posts: 3701
A square picture frame has an outer perimeter of 36 inches and is 1 in  [#permalink]

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04 Oct 2017, 13:45
Bunuel wrote:
A square picture frame has an outer perimeter of 36 inches and is 1 inch wide on all sides. What is the inner perimeter of the frame, in inches?

(A) 27
(B) 27 1/2
(C) 28
(D) 31 1/2
(E) 32

Perimeter of a square is 4s, outer perimeter = 36 inches, 4s = 36, each outer edge (side) is 36/4 = 9 inches.

The border is 1 inch wide on all sides. To find the inner perimeter of the frame, subtract two inches from each side of the outer perimeter.

Imagine a picture inside the frame that is centered (which is equivalent to the inner perimeter of a frame with a uniform border).

Between the picture and the outside perimeter of the frame, there is +1 inch above, below, to the left, and to the right of the picture. The length of the picture, e.g., has +1 on the left end and +1 on the right end.

So one side of the inner perimeter: (9 - 2) = 7 inches

There are four equal sides (the outside is a square, the border is uniform, therefore the inner perimeter is a square). P = 4s

The inner perimeter, then, in inches, is 4 * 7 = 28

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A square picture frame has an outer perimeter of 36 inches and is 1 in   [#permalink] 04 Oct 2017, 13:45
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