Question 1076236
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If a rectangular {{{highlight(cross(prisim))}}} prism  has faces of 540 {{{highlight(square)}}} in, 210 {{{highlight(square)}}} in, and 126 {{{highlight(square)}}} in, what is the volume of this box?
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<pre>
xy = 540,   (1)
yz = 210,   (2)
xz = 126.   (3)

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

{{{x^2*y^2*z^2}}} = 540*210*126,   or

{{{(x*y*z)^2}}} = 14288400.


It implies 

xyz = {{{sqrt(14288400)}}} = 3780.  (4)


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

z = {{{3780/540}}} = 7.


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

x = {{{3780/210}}} = 18.


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

y = {{{3780/126}}} = 30.


<U>Answer</U>. The dimensions of the prism are 18, 30 and 7 inches.
</pre>

Solved.