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555-605 (Medium)|   Geometry|      
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jgk
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A carpenter wants to ship a copper rod to his new construction locatio 01 Nov 2014, 14:23
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C
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74% (01:56) correct 26% (02:06) wrong based on 200 sessions

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A carpenter wants to ship a copper rod to his new construction location in his toolbox. The rod cannot be bent and has a negligible width. The rectangular tool case he is using is 12 inches wide by 16 inches long by 20 inches high. Which of the following is the longest possible rod that can fit in the toolbox?

A. 22 inches
B. 25 inches
C. 28 inches
D. 30 inches
E. 34 inches
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C
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A carpenter wants to ship a copper rod to his new construction locatio 02 Nov 2014, 07:13
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jgk

A carpenter wants to ship a copper rod to his new construction location in his toolbox. The rod cannot be bent and has a negligible width. The rectangular tool case he is using is 12 inches wide by 16 inches long by 20 inches high. Which of the following is the longest possible rod that can fit in the toolbox?

A. 22 inches
B. 25 inches
C. 28 inches
D. 30 inches
E. 34 inches
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We are basically asked to find the length of the diagonal of the solid, which is \(\sqrt{12^2+16^2+20^2}=\sqrt{800}=2-\sqrt{2}\approx{28}\).

Answer: C.
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A carpenter wants to ship a copper rod to his new construction locatio 03 Nov 2014, 23:34
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Diagonal of the box \(= \sqrt{12^2 + 16^2 + 20^2} = \sqrt{800} = \sqrt{400} * \sqrt{2} = 20 * 1.414 = 28.28\)

Answer = C
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A carpenter wants to ship a copper rod to his new construction locatio 23 Aug 2020, 18:08
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If you know how the Main Diagonal ("Deluxe" Pythagoras Theorem) is formed, this question becomes really quick.

1st Find the Diagonal of the Bottom Face.

Drawing a Diagonal through the Bottom Face Rectangle, a Pythagorean 3-4-5 Triplet Right Triangle is Formed.

The 2 Legs are 12 and 16. Thus, the Hypotenuse/Diagonal = 20

2nd, Use the Diagonal of 20 from the Bottom Face and the Back-Right Height of c = 20 as the 2 Legs of a Right Triangle. Further, use the Main Red-Dashed Diagonal as the Hypotenuse of the Right Triangle.

This is a 45-45-90 Right Triangle and the Red-Dashed Hypotenuse/Main Diagonal = 20 * Square Root of 2.

This is approximately = 28.2

C - 28 will fit

while D = 30 will NOT fit.

Answer C
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