Finding Side Lengths: Where to Begin?

[Ilikebugs]

I don't know where to start, can I find out side lengths?View attachment 6538

 

[MarkFL]

I would let $h$ be the height of the cuboid...and so the volume $V$ is given by:

\(\displaystyle V=100xyh\)

Now, if $w$ and $\ell$ are the width and length respectively, we know:

\(\displaystyle w=\frac{3y}{h}\)

\(\displaystyle \ell=\frac{\dfrac{x}{3}}{h}\)

Multiplying these two equations together, we obtain:

\(\displaystyle \ell w=\frac{xy}{h^2}\)

Now, the volume is also given by:

\(\displaystyle V=\ell wh\)

Can you now get the volume in terms of $x$ and $y$ alone?

 

[Ilikebugs]

V=100(x^2)/2y?

 

[MarkFL]

V=100(x^2)/2y?

We have:

\(\displaystyle V=100xyh=\ell wh\)

Thus:

\(\displaystyle 100xy=\ell w=\frac{xy}{h^2}\implies h^2=\frac{1}{100}\implies h=\frac{1}{10}\)

Hence:

\(\displaystyle V=100xyh=100xy\cdot\frac{1}{10}=10xy\)