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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
The figure above shows a side view of the insert and the four componen
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30 Mar 2022, 04:45
30 Mar 2022, 04:45
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The figure above shows a side view of the insert and the four components of a box designed to package four lightbulbs. The package is a rectangular box, whose base is a square with a side of 8 inches and whose height is 12 inches. A single rectangular insert is folded twice to form two identical diagonal planes, one at each end, and a horizontal plane in the middle, so that the box is divided into four identical compartments. What is the area of the insert in square inches?
A) 192
B) 224
C) \(64+4\sqrt{52}\)
D) \(64+96\sqrt{2}\)
E) \(64+128\sqrt{2}\)
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: The figure above shows a side view of the insert and the four componen
[#permalink]
07 Apr 2022, 03:07
07 Apr 2022, 03:07
Expert Reply
Explanation
We see the 8 x 12 rectangular box as shown in the figure.
A single rectangular insert is folded twice to make four identical compartments. We see in the figure that we have 4 identical right triangular compartments. So the insert is just the lightning shape shown in the figure. We need its area. It is actually a rectangle that is folded into this shape. If we open it up, we will get a rectangle and its area will be the total height * Width (which is 8 since the box has a square base of side 8)
Now, all we need is the height. Since the compartments are equal, the height of each compartment is 6. So each diagonal in the figure is 10 (using multiple of Pythagorean triplet 3-4-5).
Total height of the rectangular insert = 10 + 8 + 10 = 28
Its area = 28*8 = 224
We see the 8 x 12 rectangular box as shown in the figure.
A single rectangular insert is folded twice to make four identical compartments. We see in the figure that we have 4 identical right triangular compartments. So the insert is just the lightning shape shown in the figure. We need its area. It is actually a rectangle that is folded into this shape. If we open it up, we will get a rectangle and its area will be the total height * Width (which is 8 since the box has a square base of side 8)
Now, all we need is the height. Since the compartments are equal, the height of each compartment is 6. So each diagonal in the figure is 10 (using multiple of Pythagorean triplet 3-4-5).
Total height of the rectangular insert = 10 + 8 + 10 = 28
Its area = 28*8 = 224
gmatclubot
Re: The figure above shows a side view of the insert and the four componen [#permalink]
07 Apr 2022, 03:07
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