Geometry Q (surface area v. volume)

[neon horizon]

A rectangular prism has a smaller rectangular prism cut out from one corner. All side lengths are integers (cm). Some equal lengths are shown.

The surface area (cm2) = volume (cm3). find dimensions original prism

[young seal]

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[next lodge]

Set up equations. Preferrably let x be the common side.

[neon horizon]

i dont understand what you mean by common side

[next lodge]

The one that is congruent.

[neon horizon]

So far i tried equating the SA (which doesnt change even if cut out) and the V

So far i got 8x2+8xl = 4x2l + x2(l-x)

Where 8x2+8xl is the SA

The second part is the volume (it is cut out)

[next lodge]

Are those x's multiplication signs?

[neon horizon]

they mean x

I forgot to put ^
so x2 means x^2

[slate mango]

@neon horizon

:HelpIcon:| Help Reminder

Hello greenstumpymonster, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.

[slate mango]

@next lodge The user still needs help with this help request.

[next lodge]

That is right, yes

[neon horizon]

Lets actually plan a time to talk, im not actually available usually at your time

[next lodge]

Oh

,ti

[fluid merlin]

The current time for exiled_hype is 04:40 PM (EDT) on Mon, 16/06/2025.

[neon horizon]

I cannot work on the problem right now as i have to leave soon but its mainly i got stuck after equating the SA and the V.

Do you have any other methods to share?

[next lodge]

Not right now, but I guess you can notice that if the rectangular box was full, it would be a square prism

[neon horizon]

i already tried that to find the SA easiy

[neon horizon]

Here

[next lodge]

I mean I gave you the thumbs up, this is solvable

[neon horizon]

Could you show me how its solvable, not sure

should be an integer answer

[next lodge]

You have to equate V and SA, and then through variables you can make a system of equations

[neon horizon]

I did get one equation

You can see it above

[neon horizon]

but i dont know how to solve it

[next lodge]

I'm sorry, but I'm burned out right now and I don't feel like thinking 😭 this thread has been going on for too long