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# A rectangular solid (cuboid) has three faces, having areas 12, 45, and

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
A rectangular solid (cuboid) has three faces, having areas 12, 45, and  [#permalink]

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16 Oct 2018, 04:43
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Difficulty:

35% (medium)

Question Stats:

82% (01:43) correct 18% (02:20) wrong based on 36 sessions

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A rectangular solid (cuboid) has three faces, having areas 12, 45, and 60. What is the volume of the solid?

(A) 180
(B) 200
(C) 240
(D) 600
(E) 900

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Re: A rectangular solid (cuboid) has three faces, having areas 12, 45, and  [#permalink]

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16 Oct 2018, 04:57
Note:-
1.Each face has different areas.
2. We have to find out the measure of common side of any two faces.

HCF(12,45,60)=3=one side of the cuboid(say length)
Area face1=12=3*4=l*b
Area face2=45=3*15=l*h
Area face3=60=15*4=h*b
So l=3,b=4,and h=15

So area=l*b*h=3*4*15=180

Ans.(A)

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Re: A rectangular solid (cuboid) has three faces, having areas 12, 45, and  [#permalink]

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16 Oct 2018, 06:09
All the three values represent l*b , b*h , l*h.
Multiply all and find the square root
$$(l*b*h)^2 = √45*12*60$$
= 180
Re: A rectangular solid (cuboid) has three faces, having areas 12, 45, and   [#permalink] 16 Oct 2018, 06:09
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