A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig

Question

A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straight-line distance between any two corners of the box?

A. 22 inches
B. 25 inches
C. 28 inches
D. 30 inches
E. 34 inches

Kudos for a correct  solution .

balamoon · Answer

Answer -

The longest straight-line distance between any two corners of the box = √(W^2+L^2+H^2) = √(144+256+400) = √800

ANS C

ENGRTOMBA2018 · Answer

If L, B and H denote the Length, Breadth and Height of a cube or a cuboid, the longest straight line distance is equal to =  \sqrt{(L^2+B^2+H^2)}

Thus, per the questions, as L=16, B=12 and H=20, substituting these values , we get Longets distance = 28 inches  (=20 \sqrt{2})

GMATinsight · Answer

The longest straight-line distance between any two corners of the box =  \sqrt{L^2+B^2+H^2}  =  \sqrt{12^2+16^2+20^2}  =  \sqrt{144+256+400}  =  \sqrt{800}  = 28.3 approx.

Answer: Option C

Please see the Derivation of Longest Diagonal in a Rectangular Solid. Longest diagonal in the figure is S

AmoyV · Answer

We need the diagonal.

Diagonal =  \sqrt{12^2+16^2+20^2} 
=  \sqrt{144+256+400} 
= \sqrt{800} 
=20 \sqrt{2} 
=20*1.41
=28.2

Answer: C

robinpallickal · Answer

longest diagonal = \sqrt{l^2+b^2+h^2} = \sqrt{16^2+12^2+20^2} 
 =  \sqrt{800} 
 =  20 X \sqrt{2}  = 28 (approx)

chetan2u · Answer

although the answer is straight from formulae  \sqrt{l^2+b^2+h^2} =  \sqrt{12^2+16^2+20^2} 
the other way to look at is 12, 16 ,hyp is a right angle triange of ratio 3:4:5..
so here hyp =20.. 
now the sides are 20,20,hyp in a right angle triangle in ratio 1:1: \sqrt{2} .. hyp=20 \sqrt{2} =28
ans C

KS15 · Answer

Longest straight line distance between any two corners of the box=\sqrt{L^2+B^2+H^2}
=\sqrt{144+256+400}
=\sqrt{800}
Answer C

Bunuel · Answer

800score Official Solution:

We must first determine which two corners are furthest apart in a rectangular box. To determine the corners that are furthest apart in a rectangular box, pick any corner, and think about drawing a line through the center of the box to the furthest other corner. Let's call corners that have this relationship "opposite corners".

The distance D between any two opposite corners in a rectangular solid (whether a perfect cube or not) can be determined very quickly using the Pythagorean Theorem in a 3-dimensional manner:
D² = a² + b² + c², where a, b, and c represent the dimensions of the solid.

Now let's use the formula to determine the distance:
D² = 12² + 16² + 20²
D² = 144 + 256 + 400 = 800.

So D = √800.

Rather than trying to approximate √800, let's square the answer choices and determine which is closest to 800.

We know that 30² = 900, so the correct answer must be either choice (C) or (D). Now let's square the number in choice (C).
28² = 784.

Since 784 is much closer to 800 than 900 is,  the correct answer is choice (C).

Another way to solve this question is to use 3:4:5 triangles. Since 12:16:20 is a multiple of 3:4:5, the diagonal is 20. To find the answer, find the hypotenuse of a triangle with that diagonal and the third dimension of the box – 20 and 20, which has a hypotenuse of 20√2. √2 equals approximately 1.4, so the answer is about 28.

Bunuel · Answer

Similar question to practice: a-carpenter-wants-to-ship-a-copper-rod-to-his-new-construction-locatio-187870.html

ScottTargetTestPrep · Answer

We can use the following formula to calculate the diagonal (or d):

d^2 = 12^2 + 20^2 + 16^2

d^2 = 144 + 400 + 256

d^2 = 800

d = √800 = 20√2, so d is about 20 * 1.4 = 28.

Answer: C

Abhishek009 · Answer

\sqrt{12^2 + 16^2 + 20^2}

=  \sqrt{144 + 256 + 400}

=  \sqrt{800}

We know  30^2 = 900 , so our answer must be a bit less than 30 , among the given options only (C) 28 matches, so Answer must be (C)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards