Question

the area of three adjacent faces of a rectangular box are 2A 2B and 2c prove that volume square is equals to 8 ABC​

Answer 1

Step-by-step explanation:

volume of box = LBH = 2A×2B×2C =8ABC

Answer 2

Answer

Let dimensions be x, y and z of box

Volume will be V = xyz

Given

xy = 2A

yz = 2B

zx = 2C

Multiply all three equations

$(xy)(yz)(zx) = 8ABC \\ (xyz) {}^{2} = 8ABC \\ {V}^{2} = 8ABC\\ V= \sqrt{8ABC}$

So Volume square is 8ABC