Problem Solving

M7MBA wrote:If a rectangular box has two faces with an area of 30, two faces of area 60, and two faces of area 72, what is its volume?

A. 60
B. 90
C. 162
D. 300
E. 360

M7MBA wrote:If a rectangular box has two faces with an area of 30, two faces of area 60, and two faces of area 72, what is its volume?

A. 60
B. 90
C. 162
D. 300
E. 360

The OA is E.

Should I set a system of 3 equations here? Or, what should I do? I'd appreciate some help.

Vincen wrote:Hello M7MBA.

Here is a fast way to solve this PS question.

We know the following: $$\left(1\right)\ \ \ \ W\cdot L=30$$ $$\left(2\right)\ \ \ \ W\cdot H=60$$ $$\left(3\right)\ \ \ \ L\cdot H=72$$ Now, let's calculate the volumen squared, that is to say, $$V^2=\left(W\cdot L\cdot H\right)^2=W\cdot W\cdot L\cdot L\cdot H\cdot H$$ $$=\left(W\cdot H\right)\cdot\left(W\cdot L\right)\cdot\left(L\cdot H\right)$$ $$=\left(60\right)\cdot\left(30\right)\cdot\left(72\right)$$ $$=129600.$$ $$\Rightarrow\ \ \ V=\sqrt{129600}$$ $$\Rightarrow\ \ \ V=360.$$ Therefore, the correct answer is the option E.