If three sides of a rectangular solid have areas of 12, 18, and 24, wh

Question

If three sides of a rectangular solid have areas of 12, 18, and 24, what is the volume of the solid?

A. 72
B. 144
C. 576
D. 2,592
E. 5,184

firas92 · Answer

lb=12 
 bh=18 
 lh=24

Multiplying the three equations,

(lbh)^2 = 12*18*24 = 2*2*3*2*3*3*2*2*2*3 = 2^6*3^4 
 lbh = 2^3*3^2 = 8*9 = 72

Answer is  (A)

Ilishar · Answer

Suppose:
l*b = 12
b*h = 18
h*l = 24
Multiplying the above equations - 
(l*b*h)^2 = 12*18*24
l*b*h = 72

Option A

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ScottTargetTestPrep · Answer

We can create the equation:

LW x LH x WH = 12 x 18 x 24

L^2 x W^2 x H^2 = 12 x 18 x 24

Taking the square root, we have:

L x W x H = √12 x √18 x √24

L x W x H = 2√3 x 3√2 x 2√6

L x W x H =12√36 = 12 x 6 = 72

Alternate Solution:

To solve this problem, we need to find three numbers such that, when we pair any two of them, they will produce the products 12, 18, and 24. We can also assume the three numbers are integers. Since 3 x 4 = 12, 3 x 6 = 18 and 4 x 6 = 24, then the three integers must be 3, 4, 6, and the volume of the solid must be 3 x 4 x 6 = 72.

Answer: A

Kinshook · Answer

The sides = {4,3,6}

Volume = 4*3*6=72

IMO A

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If three sides of a rectangular solid have areas of 12, 18, and 24, wh

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If three sides of a rectangular solid have areas of 12, 18, and 24, wh

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