SOLUTION: Please help me solve this problem: A box with no top is to be constructed from a piece of cardboard whose width measures x cm and whose length measures 6 cm more than its width. Th

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Question 886812: Please help me solve this problem: A box with no top is to be constructed from a piece of cardboard whose width measures x cm and whose length measures 6 cm more than its width. The box is to be formed by cutting squares that measure 2 cm on each side from the four corners, and then folding up the sides. If the volume of the box will be 182 cm^3, what are the dimensions of the piece of cardboard?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The sides of the piece of cardboard, before
cutting out the corners, are
+x+ and +x+%2B+6+ cm
------------------------
After cutting out 2 x 2 squares from the corners,
The sides measure +x+-+2+-+2+ and
+x+%2B+6+-+2+-+2+
----------------------
+x+-+2+-+2+=+x+-+4+
+x+%2B+6++-+2+-+2+=+x+%2B+2+
--------------------------
When the 4 sides are folded up, the height of
the box will be +2+ cm, so I can say:
+%28+x+-+4+%29%2A%28+x+%2B+2+%29%2A2+=+182+ cm2
+%28+x%5E2+-+4x+%2B+2x+-+8+%29%2A2+=+182+
+x%5E2+-+4x+%2B+2x+-+8+=+91+
+x%5E2+-+2x+=+99+
Complete the square
+x%5E2+-+2x+%2B+%28+2%2F2+%29%5E2+=+99+%2B+%28+2%2F2+%29%5E2+
+x%5E2+-+2x+%2B+1+=+99+%2B+1+
+%28+x+-+1+%29%5E2+=+10%5E2+
Take the square root of both sides
+x+-+1+=+10+
+x+=+11+
+x+%2B+6+=+17+
----------------
The piece of cardboard measures 11 x 17 cm2
----------------
check:
+%28+x+-+4+%29%2A%28+x+%2B+2+%29%2A2+=+182+
+%28+11+-+4+%29%2A%28+11+%2B+2+%29%2A2+=+182+
+7%2A13%2A2+=+182+
+182+=+182+