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UKMT Volume = Surface Area (Cuboid) Question

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I got 42 as the answer but I felt like my method was really inefficient, this is what I did:

Labeled the two other sides as aa and bb.
Surface Area = Volume
6b+6a+2ba=3ba[br]6b+6a=ba6b + 6a +2ba = 3ba[br]6b + 6a = ba
And the smaller bb is the larger aa is and the first value of bb that doesn't give a negative value of aa is 77, so a=42a = 42.

Is this right? If so is it the most efficient method?

Thanks in advance
Original post by Retsek
Capture.PNG
I got 42 as the answer but I felt like my method was really inefficient, this is what I did:

Labeled the two other sides as aa and bb.
Surface Area = Volume
6b+6a+2ba=3ba[br]6b+6a=ba6b + 6a +2ba = 3ba[br]6b + 6a = ba
And the smaller bb is the larger aa is and the first value of bb that doesn't give a negative value of aa is 77, so a=42a = 42.

Is this right? If so is it the most efficient method?

Thanks in advance


It is correct but i'm not sure of a more efficient method.
Original post by Retsek
x


This is fine but if you want to be more formal, you could say that without loss of generality a>ba>b. Then a=6bb−6=6+36b−6\displaystyle a=\frac{6b}{b-6}= 6+\frac{36}{b-6} so as bb gets larger aa gets smaller. So now you just need to find the smallest integer bb that makes aa an integer as well, which you have done.
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Retsek
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Original post by I hate maths
This is fine but if you want to be more formal, you could say that without loss of generality a>ba>b. Then a=6bb−6=6+36b−6\displaystyle a=\frac{6b}{b-6}= 6+\frac{36}{b-6} so as bb gets larger aa gets smaller. So now you just need to find the smallest integer bb that makes aa an integer as well, which you have done.


Ah see this was where I was going wrong before I had that equation but kept getting a = -6 so went at it from a different angle

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