I really need your help!

[CMW]

Ok so I'm in this after school math class that is a grade above my current grade level. The teacher recently gave us this problem. She never said we couldn't ask for outside help, so don't feel guilty helping me out.

Here's the problem:

Suppose you had baked a tray of brownies. Half for a friend and half for yourself. Your little brother comes along and cuts a rectangular piece out of the tray(keep in mind this can be any random place on the tray) How could you divide the remaining portion to be exactly 2 equal pieces in JUST 1 CUT?

Remember:
Don't think of it 3 dimensionally. You dont slice it heightwise.
It's probabley a formula and it will work for ANY problem no matter where the cut is.
It could be in terms of x
My teacher said once we know the answer, we will kick ourselves for not knowing it.

 

[Gene]

How about:
Slide the tray to the edge of the table till it just starts to tip (don't let it fall) then cut along the edge.
Or balance it on a rolling pin then cut in a line with the pin.
Or hold a string at the corner of the pan with a weight on the end and let the pan swing free. Cut along the string.
It's not exactly math but it's the best that can be done (as long as the pan is light compared to the cake.)
------------------
Gene

 

[Denis]

I assume it's like a cake; simply remove from tray, measure thickness,
then cut horizontally at halfway mark; example:
12 inches long by 10 inches wide by 4 inches thick:
cut horizontally at 2 inches; end up with 2 pieces 12 by 10 by 2 : kick yourself!!

 

[Gene]

Denis, read the whole post. "don't think three demensionaly."
G

 

[Denis]

Whoops...
Your ways sure seem good, Gene.

As far as "in terms of x":
measure cake top to get area ; 10 by 12 = 120 sq. in.
measure triangle sides to get area; assume 12 sq. in.
find spot where cutting with 1 cut will produce half of remainder:
120 - 12 = 108
12x = 54
x = 4.5
So cut at 4.5 of width to get a piece 4.5 * 12 = 54

Depends where triangle is.
But then possibly impossible if li'l brother cut out a very large triangle

HEY! Could be li'l brother was considerate and cut his triangle from 2 corners to middle of opposite side:
then NO cut required :roll: