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A rectangular box has a length of 6 centimeters, a width of
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06 Oct 2018, 15:18
06 Oct 2018, 15:18
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Question Stats:
90% (00:49) correct
9% (01:24) wrong based on 51 sessions
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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) \(24\)
(A) \(10\)
(B) \(12\)
(C) \(10\sqrt{2}\)
(D) \(10\sqrt{3}\)
(E) \(24\)
Re: A rectangular box has a length of 6 centimeters, a width of
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30 Mar 2020, 15:18
30 Mar 2020, 15:18
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The diagonal of a rectangular box is the square root of length squared + width squared + height squared.
Re: A rectangular box has a length of 6 centimeters, a width of
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15 Jun 2021, 22:21
15 Jun 2021, 22:21
2
A fast approach to solving this problem is to use the “Super Pythagorean theorem,” which states that the diagonal of any rectangular box
is d in the following formula:
d2 = l2 + w2 + h2
where l, w, and h are the length, width, and height of the box, respectively.
Plugging in the given information yields:
d2 = 62 + 82 + 102
d2 = 36 + 64 + 100
d2 = 200
Alternatively, if you don’t remember the Super Pythagorean, apply the normal
Pythagorean theorem twice. To find the diagonal of the box, first find the
diagonal of one of the sides. Use the bottom side of the figure below as the
base:
Applying the
Pythagorean theorem:
c2 = a2 + b2
c2 = 62 + 82
c2 = 36 + 64
c2 = 100
c = 10
From here, draw the diagonal of the box and apply the Pythagorean theorem
again to the vertically oriented triangle with legs 10 and 10 again
d2 = 102 + 102
d2 = 100 + 100
d2 = 200
d=10sqrt(2)
is d in the following formula:
d2 = l2 + w2 + h2
where l, w, and h are the length, width, and height of the box, respectively.
Plugging in the given information yields:
d2 = 62 + 82 + 102
d2 = 36 + 64 + 100
d2 = 200
Alternatively, if you don’t remember the Super Pythagorean, apply the normal
Pythagorean theorem twice. To find the diagonal of the box, first find the
diagonal of one of the sides. Use the bottom side of the figure below as the
base:
Applying the
Pythagorean theorem:
c2 = a2 + b2
c2 = 62 + 82
c2 = 36 + 64
c2 = 100
c = 10
From here, draw the diagonal of the box and apply the Pythagorean theorem
again to the vertically oriented triangle with legs 10 and 10 again
d2 = 102 + 102
d2 = 100 + 100
d2 = 200
d=10sqrt(2)
