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In the figure above, a regular octagon with a side of 2 inches is surrounded by eight identical right triangles whose

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In the figure above, a regular octagon with a side of 2 inches is surrounded by eight identical right triangles whose

by M7MBA » Fri Dec 11, 2020 2:37 am

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In the figure above, a regular octagon with a side of 2 inches is surrounded by eight identical right triangles whose legs are 3 and 4 inches. What is the largest possible perimeter of the shape formed?

A) 24
B) 32
C) 40
D) 48
E) 64

Answer: E

Source: Economist
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Re: In the figure above, a regular octagon with a side of 2 inches is surrounded by eight identical right triangles whos

by swerve » Sun Dec 13, 2020 1:18 pm
M7MBA wrote: ↑
Fri Dec 11, 2020 2:37 am
 gmatbusters (3).jpg

In the figure above, a regular octagon with a side of 2 inches is surrounded by eight identical right triangles whose legs are 3 and 4 inches. What is the largest possible perimeter of the shape formed?

A) 24
B) 32
C) 40
D) 48
E) 64

Answer: E

Source: Economist
Perimeter (exposed lengths) for one triangle \(= 4\) (from one side) \(+ \big[5 - (3-2)\big]\) (from hypotenuse) \(= 4 + 4 = 8\)

Total perimeter \(= 8\cdot 8\) (\(8\) triangles) \(= 64\) inches
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Re: In the figure above, a regular octagon with a side of 2 inches is surrounded by eight identical right triangles whos

by Scott@TargetTestPrep » Mon Dec 14, 2020 7:25 am
M7MBA wrote: ↑
Fri Dec 11, 2020 2:37 am
 gmatbusters (3).jpg

In the figure above, a regular octagon with a side of 2 inches is surrounded by eight identical right triangles whose legs are 3 and 4 inches. What is the largest possible perimeter of the shape formed?

A) 24
B) 32
C) 40
D) 48
E) 64

Answer: E

Solution:

The perimeter of the shape formed consists of two types of sides: the 4 inch leg of a right triangle and a portion of the hypotenuse of a right triangle. If we can determine the length of the latter type of a side, we can determine the perimeter of the shape. Let this unknown length be x.

Notice that the hypotenuse of each right triangle consists of a line segment of length x and a portion of a 3 inch leg. Notice also that the part of each 3 inch leg which does not overlap with a hypotenuse is a side of the regular octagon, which has length 2. Thus, the part of a 3 inch leg which overlaps with a hypotenuse has length 3 - 2 = 1. It follows that x equals 5 - 1 = 4.

Since there are 8 right triangles, there are 8 legs of length 4 and 8 sides with length x = 4. It follows that the perimeter of the shape is 8 x 4 + 8 x 4 = 64.

Answer: E

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