Let the volume, surface area and length of the diagonal of a cuboid be as follows: $144$, $192$, $13$. Find the dimensions.
My trial: $$lbh = 144$$
$$2(lb+bh+lh) = 192 \implies lb+bh+lh = 96$$
$$l^2 + b^2 + h^2 = 13^2 = 169.$$
As $(l+b+h)^2 = l^2 + b^2 + h^2 + 2(lb+bh+lh) = 169 + 192 = 361$. So, $l+b+h = 19$.
Then?
NB: Sorry to all for posting my 1st question in a wrong manner. Thanks for helping me.
Best Answer
lsp's answer is a special case of Vieta's formula for cubics.