Can you cut a cake fairly to solve this middle school math problem?

[Losty]

Exactamundo.  But to elaborate

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Of course every one of the triangles have the same height regardless of where their base may be.  For those which straddle a corner, each can be dissected into two triangles with a common height whose bases sum to the same as the other.  So for a square with side length = 20, the base of each triangle must be 4(20)/5 = 16  and the combined sides of a piece which includes a corner, like your red one, where 12 + 4 = 16.  Since the height of both triangles remains 8, the combined area of the two triangles would be 12(8)/2 + 4(8)/2 which can be rewritten as (12 + 8)(8)/2.

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If that's what Losty has to do, none of you are getting equal portions of cake. Apologies Losty.

Mathing is a sin anyway so I'm not offended. I figured we'd find something more fun to do than cutting a cake

[vorlon13]

Dress up and go out tonight ??

[flagbears]

Why can't Losty make 5 cakes ??


She lazy or sumthin' ??

 

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5 cuts. Each running from the center to the outside edge. In the case of a 20 x 20 x 5 cake each cut needs to be 16 linear centimeters along the outside edge. That would give everyone 160 square centimeters of icing and 400 cubic centimeters of cake.

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Mathematically this is a easy and clear solution, but I rejected it because I missed the part about the cake being a square, and thought the original question indicated the dimension, and presumably the aspect ratio, of the cake didn't matter.  This implies the solution had to be elegant enough to not require careful measurements of the aspect ratio of the cake to come up with angles of the cuts.

That's an optical illusion, wtf!

[Alex K]

Did you just necro all threads with math in them?

[Edwardo Piet]

This guy is a mathsive prick.

[Dropship]

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5 cuts. Each running from the center to the outside edge. In the case of a 20 x 20 x 5 cake each cut needs to be 16 linear centimeters along the outside edge. That would give everyone 160 square centimeters of icing and 400 cubic centimeters of cake.

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Hey wait a minute, ain't it cheating to use a ruler to meaure precise distances?
And if a ruler is allowed, wouldn't it be far simpler to just make straight cuts right across the cake at 4cm intervals to get 5 rectangular slices or have I got my maths wrong?

[chimp3]

I don't have the patience for this , so here:

[popeyespappy]

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5 cuts. Each running from the center to the outside edge. In the case of a 20 x 20 x 5 cake each cut needs to be 16 linear centimeters along the outside edge. That would give everyone 160 square centimeters of icing and 400 cubic centimeters of cake.

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Hey wait a minute, ain't it cheating to use a ruler to meaure precise distances?
And if a ruler is allowed, wouldn't it be far simpler to just make straight cuts right across the cake at 4cm intervals to get 5 rectangular slices or have I got my maths wrong?

If you do it your way everyone is going to get the same amount of cake, but the 2 people on the ends are going to get a lot more icing than the 3 in the middle.

[Jackalope]

Hey wait a minute, ain't it cheating to use a ruler to meaure precise distances?
And if a ruler is allowed, wouldn't it be far simpler to just make straight cuts right across the cake at 4cm intervals to get 5 rectangular slices or have I got my maths wrong?

If you do it your way everyone is going to get the same amount of cake, but the 2 people on the ends are going to get a lot more icing than the 3 in the middle.

Wait, you haven't accounted for the thickness of the frosting. Yeah the slices on the end will have more frosting, but they'll habe less cake by whatever depth the frosting is.

[Whateverist]

If that's what Losty has to do, none of you are getting equal portions of cake. Apologies Losty.

Mathing is a sin anyway so I'm not offended. I figured we'd find something more fun to do than cutting a cake

Fine. I challenge you to a cheese cutting contest. Small hermetically sealed room, no masks.

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If you do it your way everyone is going to get the same amount of cake, but the 2 people on the ends are going to get a lot more icing than the 3 in the middle.

Wait, you haven't accounted for the thickness of the frosting.   Yeah the slices on the end will have more frosting, but they'll habe less cake by whatever depth the frosting is.

So this solution has even more problems.  Interesting.