MHB 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:

$$V=100xyh$$

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

$$w=\frac{3y}{h}$$

$$\ell=\frac{\dfrac{x}{3}}{h}$$

Multiplying these two equations together, we obtain:

$$\ell w=\frac{xy}{h^2}$$

Now, the volume is also given by:

$$V=\ell wh$$

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:

$$V=100xyh=\ell wh$$

Thus:

$$100xy=\ell w=\frac{xy}{h^2}\implies h^2=\frac{1}{100}\implies h=\frac{1}{10}$$

Hence:

$$V=100xyh=100xy\cdot\frac{1}{10}=10xy$$