SOLUTION: If a rectangular prisim has faces of 540 in,210in, and 126in, what is the volume of this box?

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Question 1076236: If a rectangular prisim has faces of 540 in,210in, and 126in, what is the volume of this box?
Answer by ikleyn(52832) About Me  (Show Source):
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If a rectangular highlight%28cross%28prisim%29%29 prism has faces of 540 highlight%28square%29 in, 210 highlight%28square%29 in, and 126 highlight%28square%29 in, what is the volume of this box?
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xy = 540,   (1)
yz = 210,   (2)
xz = 126.   (3)

Multiply the three equations (both sides). You will get

x%5E2%2Ay%5E2%2Az%5E2 = 540*210*126,   or

%28x%2Ay%2Az%29%5E2 = 14288400.


It implies 

xyz = sqrt%2814288400%29 = 3780.  (4)


Now divide eq(4) by eq(1) (both sides). You will get

z = 3780%2F540 = 7.


Next, divide eq(4) by eq(2) (both sides). You will get

x = 3780%2F210 = 18.


Finally, divide eq(4) by eq(3) (both sides). You will get

y = 3780%2F126 = 30.


Answer. The dimensions of the prism are 18, 30 and 7 inches.

Solved.