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
OA is C
Not sure whether it is correct..I thought it is E
Any light into this?
square picture
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sairamGmat 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
OA is C
Not sure whether it is correct..I thought it is E
Any light into this?
AB + BC + CD + DA = 36 in.
As shown in the figure, from each side we'll subtract 2 in.. which means we subtract 8 from the perimeter of the outer square to get the perimeter of the inner square.
So, 36 - 8 = 28 in.
The correct answer is [spoiler](C)[/spoiler].
Rahul Lakhani
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Outer perimeter = 36 => outer square side = 9
inner square is layed out in such a way it leaves 1 inch width on all its sides
inner square side = 9 - 1-1 = 7
permiter of inner square = 4*7 =28
Answer is C.
inner square is layed out in such a way it leaves 1 inch width on all its sides
inner square side = 9 - 1-1 = 7
permiter of inner square = 4*7 =28
Answer is C.
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the solution given by rahul is perfect.
if you thought that the inner frame was 8 x 8, then that means you didn't draw a diagram! if you draw even a crude diagram of the situation, it becomes quite obvious that you need to subtract 2 inches, not just 1 inch, from each side of the original square.
ALWAYS draw diagrams for geometry problems that don't already have diagrams!
if you thought that the inner frame was 8 x 8, then that means you didn't draw a diagram! if you draw even a crude diagram of the situation, it becomes quite obvious that you need to subtract 2 inches, not just 1 inch, from each side of the original square.
ALWAYS draw diagrams for geometry problems that don't already have diagrams!
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side of outer frame = 36/4 = 9
subtract 1 twice from the outer frame to get the inner frame side= 9-2 = 7
perimeter = 7*4 = 28
subtract 1 twice from the outer frame to get the inner frame side= 9-2 = 7
perimeter = 7*4 = 28
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There is a cool formula for solving such problem as follows :sairamGmat 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
OA is C
Not sure whether it is correct..I thought it is E
Any light into this?
Outer Perimeter = P
Width of the Square is = w
So Inner Perimeter is :
{ p / 4 - 2*w } * 4
Applying the formula :
P = 36
w = 1
So { p / 4 - 2*w } * 4
{36 / 4 - 2* ( 1 )}* 4
( 9 - 2 ) * 4
28 inches...
The logic behind it is very well explained by other users , so not going in such details...
Abhishek
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