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While solving a problem about volumes of parallelepipeds, I came across three expressions involving the products of its respective sides: $a,b$ and $c$. The equations are the following:

$ab = 60$

$ac = 40$

$bc = 24$

Now I want to find the volume of the parallelepiped $V=abc$. Is there an elegant way to do so from these equations? Thank you in advance.

Uri Toti
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2 Answers2

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Multiply all three equations together and take the square root of both sides of the resulting equation.

Phillip Feldman
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Hint: Letting $x=\frac{20}a$, the first two equations give that $b=3x$ and $c=2x$, putting this into the third one: $6x^2=24$.

Berci
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  • Yes, that is definitely a way, but I wanted to look for a more elegant one. Nevertheless, thank you. – Uri Toti May 01 '22 at 19:20