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Question:
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) 27.5
(C) 28
(D) 31.5
(E) 32
Approach Solution 1
Each outside side of the SQUARE frame is 9 inches if the outer circumference is 36 inches (because 9 + 9 + 9 + 9 = 36).
Since we lose 1 inch on both sides, the inner side of the frame will be 2 inches shorter on each side.
Consequently, the length of each inner side of the frame will be 7 inches.
The inner perimeter of the frame therefore equals 7 + 7 + 7 + 7 = 28 equals C.
Sum of all sides equals 36 for the outer square's perimeter.
Since the square's sides are all equal, the side of the outer square is 36/4, or 9.
The side of the inner square is 9-1-1, which equals 7, and the perimeter of the inner square is the sum of all its sides, which equals 7+7+7+7, which is 28.
C is the correct answer.
Approach Solution 2
A square's perimeter is 4s, its outer perimeter is 36 inches, 4s is 36, and each of its four sides' outer edges is 36/4, or 9 inches.
On all sides, the border is one inch broad. Subtract two inches from each side of the outer perimeter to get the frame's inner perimeter.
The inner perimeter of a frame with a uniform border is equivalent to a picture that is centred inside the frame.
There is one inch above, below, to the left, and to the right of the photo between it and the edge of the frame. For instance, the length of the image has +1 on the left and +1 on the right.
Thus, the inner perimeter's one side measures: (9 - 2) = 7 inches.
There are four equal sides (the inner perimeter is square since the border is uniform and the outer is square). P = 4s
Therefore, the inner perimeter is 4 * 7 = 28 in inches.
C is the correct answer.
Approach Solution 3
The inner square's sides are 7 inches in the illustration below.
Therefore, the inner square's perimeter is 7 * 4 = 28 inches.
The appropriate answer is C.
“A square picture frame has an outer perimeter of 36 inches and is 1 inch wide on all sides" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.
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