SOLUTION: Rachel cut a square cake vertically to make two rectangle slices. Each rectangle had a perimeter of 51 inches.How long is each side of the original square cake?

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Question 1158526: Rachel cut a square cake vertically to make two rectangle slices. Each rectangle had a perimeter of 51 inches.How long is each side of the original square cake?
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
rectangle's length is the same as the side of the square.
The rectangles are equal, so the width of each rectangle is half the side of the square or half the length of the rectangle.
length+width=1/2 of the perimeter=25.5 in
L+(.5L)=25.5, by substitution
L=25.5/1.5=17 inches
so the sides of the square are each 17 inches
the rectangles made are 17 inches x 8.5 inches. That is a half-perimeter of 25.5 or a perimeter of 51 inches

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Formula for perimeter of each rectangle:
+P+=+2W+%2B+2L+
Let +L+ = the original side of the square
+W+=+%28+1%2F2+%29%2AL+
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For one of the 2 rectangles:
+2%2A%28+1%2F2%29%2AL+%29+%2B+2L+=+51+
+L+%2B+2L+=+51+
+3L+=+51+
+L+=+17+
A side of the original square cake is 17 inches
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check:
+P+=+2W+%2B+2L+
+51+-+2W+%2B+2%2A17+
+2W+=+51+-+34+
+2W+=+17+
Correct because th cake was cut in half