The total area of all the faces of a cuboid is 22 cm2, and the total length of all its edges is 24 cm. Find the length of any one of its internal diagonals.

I can't seem to get this, so any help appreciated

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- Oct 17th 2011, 07:32 AMBobtheBobDiagonal of a Cuboid
The total area of all the faces of a cuboid is 22 cm2, and the total length of all its edges is 24 cm. Find the length of any one of its internal diagonals.

I can't seem to get this, so any help appreciated - Oct 17th 2011, 07:53 AMPlatoRe: Diagonal of a Cuboid
- Oct 17th 2011, 08:42 AMBobtheBobRe: Diagonal of a Cuboid
Ok thanks for the reply. I've already managed to get these equations from the question:

22=2(ab+ac+bc)

24=4(a+b+c)

d= http://latex.codecogs.com/png.latex?...b%5E2+c%5E2%7D.

but I can't manage to work out how to get the lengths? - Oct 17th 2011, 08:55 AMPlatoRe: Diagonal of a Cuboid
- Oct 17th 2011, 09:07 AMBobtheBobRe: Diagonal of a Cuboid

Ok, thanks for the tip.

Where have you got $\displaystyle (a+b+c)^2$ from? I'm really sorry but I think I'm being a bit slow today. (Speechless)

I know that $\displaystyle a^2+b^2+c^2=Diagonal$ because you get that from pythagorus' theorum, but where do you get $\displaystyle (a+b+c)^2$ and $\displaystyle (a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc$ from?

Thanks again and sorry that I'm being a bit slow today. - Oct 17th 2011, 09:16 AMPlatoRe: Diagonal of a Cuboid
- Oct 17th 2011, 09:22 AMBobtheBobRe: Diagonal of a Cuboid
Oh right so $\displaystyle a^2+b^2+c^2=36$?!

- Oct 17th 2011, 09:25 AMPlatoRe: Diagonal of a Cuboid
- Oct 17th 2011, 09:59 AMBobtheBobRe: Diagonal of a Cuboid
- Oct 17th 2011, 10:07 AMBobtheBobRe: Diagonal of a Cuboid
Oh right of course!

So

$\displaystyle 2ab+2ac+2bc=22$

$\displaystyle 4a+4b+4c=24$

Therefore $\displaystyle a+b+c=6$

Then, $\displaystyle (a+b+c)^2=36$

$\displaystyle a^2+b^2+c^2+2ab+2ac+2bc=36$

So sub in $\displaystyle 22=2ab+2ac+2bc$

$\displaystyle 36=a^2+b^2+c^2 +22$

$\displaystyle a^2+b^2+c^2=14$

Therefore,

$\displaystyle \sqrt{a^2+b^2+c^2}=\sqrt{14}$

So the diagonal is**$\displaystyle \sqrt{14}$**as $\displaystyle d=\sqrt{a^2+b^2+c^2}$

Thanks so much for the help! It's really obvious when you know. (This is right though?) (Happy)