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#1 2008-05-25 20:40:45

BL5965
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Geometry problem involving cakes: Please help using equations

Okay, here is the question, it is a word problem.

Jill's birthday cake is square with side length of 20cm. She cuts it with 4 straight line cuts all intersecting at a point 'P' and and at 45 degrees to one another with 2 of the cuts parallel to the sides of the cake. Thus the cake is cut into 8 pieces for the boys and girls at her party. She marks 'B' for a boy's piece and 'G' for a girl's piece around the point P. Of course, not every individual necessarily gets the same amount of cake.

1a) Show that if P is any point on the cake, the boys and girls will collectively receive the same amount of cake.

1b) Show that if P is on a main diagonal on the cake, the boys and girls will collectively receive the same amount of cake.     

1c) Show that if P is 8cm from one side and 6cm from the other side of the cake, the boys and girls will collectively receive the same amount of cake.

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