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A rectangular cardboard is to be made into an open box by cutting 2 cm square piece from each corner and turning up the sides.
\n" ); document.write( " If the perimeter of the cardboard is 60 cm. and the volume of the resulting box is 224 cm^3, what are the dimensions of the cardboard.
\n" ); document.write( ":
\n" ); document.write( "The perimeter of the base equation
\n" ); document.write( "2L + 2W = 60
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "L + W = 30
\n" ); document.write( "Use this form for substitution
\n" ); document.write( "L = (30-W)
\n" ); document.write( ":
\n" ); document.write( "We know the height of the box will be 2 inches, divide the vol by 2 and we can just solve for the area of the base which would be 112 sq/in
\n" ); document.write( ":
\n" ); document.write( "(L-4)*(W-4) = 112
\n" ); document.write( "replace L with (30-W)
\n" ); document.write( "((30-W)-4)*(W-4) = 112
\n" ); document.write( "(-W+26)(W-4) = 112
\n" ); document.write( "FOIL
\n" ); document.write( "-W^2 + 4W + 26W - 104 = 112
\n" ); document.write( "-W^2 + 30W - 104 - 112 = 0
\n" ); document.write( "-W^2 + 30W - 216 = 0
\n" ); document.write( "Multiply equation by -1, easier to factor
\n" ); document.write( "W^2 - 30W + 216 = 0
\n" ); document.write( "(W-12)(W-18) = 0
\n" ); document.write( "Two valid solutions
\n" ); document.write( "W = 12' then L
\n" ); document.write( "W = 18
\n" ); document.write( ":
\n" ); document.write( "The dimensions of the card board 18 by 12
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this by finding the vol, subtract 4\" from the dimensions:
\n" ); document.write( "14*8*2 = 224 \n" ); document.write( "