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A rectangular box has a length of 6 centimeters, a width of 8 centimet

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A rectangular box has a length of 6 centimeters, a width of 8 centimet  [#permalink]

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New post 11 Oct 2018, 01:57
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A rectangular box has a length of 6 centimeters, a width of 8 centimeters, and a height of 10 centimeters. What is the length of the diagonal of the box, in centimeters?


(A) \(10\)

(B) \(12\)

(C) \(10\sqrt{2}\)

(D) \(10\sqrt{3}\)

(E) \(24\)

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A rectangular box has a length of 6 centimeters, a width of 8 centimet  [#permalink]

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New post 11 Oct 2018, 03:30
Bunuel wrote:
A rectangular box has a length of 6 centimeters, a width of 8 centimeters, and a height of 10 centimeters. What is the length of the diagonal of the box, in centimeters?


(A) \(10\)

(B) \(12\)

(C) \(10\sqrt{2}\)

(D) \(10\sqrt{3}\)

(E) \(24\)


Longest Diagonal of the Box \(= √(l^2+b^2+h^2) = √(6^2+8^2+10^2) = √200 = 10√2\)

Answer: Option C
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Re: A rectangular box has a length of 6 centimeters, a width of 8 centimet  [#permalink]

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New post 11 Oct 2018, 06:56
Bunuel wrote:
A rectangular box has a length of 6 centimeters, a width of 8 centimeters, and a height of 10 centimeters. What is the length of the diagonal of the box, in centimeters?


(A) \(10\)

(B) \(12\)

(C) \(10\sqrt{2}\)

(D) \(10\sqrt{3}\)

(E) \(24\)


\(Diagonal = \sqrt{6^2 + 8^2 + 10^2}\)

Or, \(Diagonal = \sqrt{200}\)

Or, \(Diagonal = 10\sqrt{2}\) ; Answer must be (C)
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Re: A rectangular box has a length of 6 centimeters, a width of 8 centimet  [#permalink]

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New post 13 Oct 2018, 17:45
Bunuel wrote:
A rectangular box has a length of 6 centimeters, a width of 8 centimeters, and a height of 10 centimeters. What is the length of the diagonal of the box, in centimeters?


(A) \(10\)

(B) \(12\)

(C) \(10\sqrt{2}\)

(D) \(10\sqrt{3}\)

(E) \(24\)


We can use the formula to determine the length d of the diagonal:

l^2 + w^2 + h^2 = d^2

6^2 + 8^2 + 10^2 = d^2

36 + 64 + 100 = d^2

200 = d^2

√100 x √2 = d

10√2 = d

Answer: C
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Re: A rectangular box has a length of 6 centimeters, a width of 8 centimet   [#permalink] 13 Oct 2018, 17:45
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