Question 1044201
Q:
What is the volume of a rectangular box if three of its faces have areas of 30,70 and 84? 
Solution:
Let L, W, and H be the length, width, and height respectively of the rectangular box.
LW = 30
LH = 70 and
HW = 84
Multiply the 3 equations
(LW)(LH)(HW) = (30)(70)(84)
{{{(LWH)^2 = 176400}}}
Get the square root of both sides.
LWH = {{{sqrt(176400)}}} = 420
Therefore, the volume of the box is {{{highlight(420)}}} cubic units.