Another quite tricky maths problem: re area

[Bink]

Challenge: sketch a cuboid with a total surface area of 600 cm squared.

(Note: not a cube.)

By trial & error ds and I found a solution that gave us 598 cm squared (and I can sort of see with some millimetre-fiddling we could have got it up to 600, but we were tired out by then) - but, O maths genii, does it have to be done by trial & error - or - can you devise a formula to produce the set of potential answers?

Virtual bottle of champagne (or even real , should we ever meet) to anyone who can do this!

ok -
cuboid has two of each face. Each face has two dimensions and there are 3 dimensions overall - a b c.

So 2ab+2ac+2bc=600
ab+ac+bc=300

Now you can choose two of your dimensions and let the third be the variable one.

So I randomly chose a=10 b=5

Which gives you (plugging those into formula)

50+10C+5C=300
which is
15C=250
C= 16.67cm.

You can do that for any a and b.

hope that helps.

pssst.
I love champagne

Goodness me. Thank you, and thank you especially for setting it out so clearly - ds will be delighted.

plus, necessarily, an IOU for if we ever meet!

very nice champagne - thank you!

btw - you and your son are very welcome

Just a further update ...

Ds said your solution was "the cleverest formula I've ever heard": a very happy boy!

Inspired by it (this is the whole point of formula-thinking, I think, that you then hit on your own), he then produced this [h means "height", w means "width", d means "depth"]:

d = ((area divided by 2) - hw) divided by (h + w)

so let's say (this was his example) h and w are both 5; area is 600 of course

ie d = (300 - (5 x 5)) divided by (5 + 5)

so d = 27.5

(This is better for my brain than any amount of Wiiiiii training)

awww thats brilliant I'm really impressed that he then took it further so he had his own work to take in - tell him hes a fab lad!