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The areas of three faces of a rectangular solid are 12, 15 and 20. Wha

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Carcass
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The areas of three faces of a rectangular solid are 12, 15 and 20. Wha [#permalink] New post   16 Jun 2021, 04:28
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The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid?

A. 30
B. 60
C. 180
D. 900
E. 3600
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B
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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha [#permalink] New post   16 Jun 2021, 05:10
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Carcass wrote:
The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid?

A. 30
B. 60
C. 180
D. 900
E. 3600


Let x = the width
Let y = the length
Let z = the height
So, the volume = xyz

Area of one face = 12
We can write: xy = 12

Area of one face = 15
We can write: xz = 15

Area of one face = 20
We can write: yz = 20

Combine to get: (xy)(xz)(yz) = (12)(15)(20)
Simplify: x²y²z² = 3600
Rewrite as: (xyz)² = 60²
So, xyz = 60
In other words, the volume = 60

Answer: B

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Brent
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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha [#permalink] New post   29 Jul 2023, 13:42
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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha [#permalink]
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