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655-705 (Hard)|   Geometry|      
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In the figure above, a regular octagon with a side of 2 inches is surr 01 Jul 2018, 18:27
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55% (hard)

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60% (02:04) correct 40% (02:30) wrong based on 72 sessions

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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
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E
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In the figure above, a regular octagon with a side of 2 inches is surr 01 Jul 2018, 18:46
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IMO E. 64
Part of hypotenuse is 5+2-3=4
8 sides of length 4 (part of hypotenuse)
8 sides of length 4 (leg)
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In the figure above, a regular octagon with a side of 2 inches is surr 01 Jul 2018, 19:37
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Option E, IMO

Perimeter (exposed lengths) for one triangle = 4 (from one side) + {5 - (3-2)} (from hypotenuse) = 4+ 4 = 8
Total perimeter = 8*8 (8 triangles) = 64 inches
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In the figure above, a regular octagon with a side of 2 inches is surr 02 Jul 2018, 06:51
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We can use the Pythagorean triplet 3-4-5: the triangles' hypotenuses are 5.
i) The part of the hypotenuse which is part of the perimeter is 5 minus [part of the triangle's leg of 3]: 5 —1 = 4
ii) The leg of triangle which is part of perimeter is 4.
Since there are 8 triangles, the perimeter is 8 [leg of 4 + part of hypotenuse which is included in perimeter] = 8 (4+4) = 64
Answer (E) 64 .
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In the figure above, a regular octagon with a side of 2 inches is surr 19 Dec 2020, 17:28
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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
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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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