document.write( "Question 772989: Find the dimensions of a rectangular prism with a volume of 162 cubic m if the width is 1/2 the length and the height is three times the width. \n" ); document.write( "
Algebra.Com's Answer #471242 by pakhi(24)\"\" \"About 
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A rectangular prism is one which has two rectangles as its two end faces.
\n" ); document.write( "Volume of a rectangular prism is given by the formula
\n" ); document.write( "Volume(V) = Area(A) of one of its rectangles * Height(H) of the prism
\n" ); document.write( "Let the length of the rectangle be 'L' meters
\n" ); document.write( "Let the width of the rectangle be 'W' meters
\n" ); document.write( "Then the area(A) of the rectangle is = length * width = LW square meters
\n" ); document.write( "But from the problem we find that W = (1/2)L
\n" ); document.write( "Also the height(H) of the prism = 3W = 3*(1/2)L = (3/2)L
\n" ); document.write( "So the volume(V) = A * H = L * (1/2)L * (3/2)L = (3/4)L^3
\n" ); document.write( "But V = 162 cubic meters
\n" ); document.write( "So (3/4)L^3 = 162
\n" ); document.write( "or L^3 = 162 * (4/3) = 54 * 4 = 2 * 27 * 4
\n" ); document.write( "or L * L * L = 2 * 2 * 2 * 3 * 3 * 3
\n" ); document.write( "or L = 6 meters
\n" ); document.write( "So W = (1/2)L = (1/2)6 = 3 meters
\n" ); document.write( "So H = (3/2)L = (3/2)6 = 9 meters
\n" ); document.write( "Therefore the dimensions of the rectangular prism is
\n" ); document.write( " Length = 6m
\n" ); document.write( " Width = 3m
\n" ); document.write( " Height = 9m
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\n" ); document.write( "\n" ); document.write( "Check: V = A * H = L * W * H = 6 * 3 * 9 = 162
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