document.write( "Question 772990: What are the dimensions of a rectangular prism with a volume of 576 cubic m if the width is 3/4 the length and the height is twice the width? \n" ); document.write( "
Algebra.Com's Answer #471239 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 = (3/4)L
\n" ); document.write( "Also the height(H) of the prism = 2W = 2*(3/4)L = (3/2)L
\n" ); document.write( "So the volume(V) = A * H = L * (3/4)L * (3/2)L = (9/8)L^3
\n" ); document.write( "But V = 576 cubic meters
\n" ); document.write( "So (9/8)L^3 = 576
\n" ); document.write( "or L^3 = 576 * (8/9) = 64 * 8
\n" ); document.write( "or L * L * L = 8 * 8 * 8
\n" ); document.write( "or L = 8 meters
\n" ); document.write( "So W = (3/4)L = (3/4)8 = 6 meters
\n" ); document.write( "So H = (3/2)8 = (3/2)8 = 12 meters
\n" ); document.write( "Therefore the dimensions of the rectangular prism are
\n" ); document.write( " Length = 8m
\n" ); document.write( " Width = 6m
\n" ); document.write( " Height = 12m
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\n" ); document.write( "\n" ); document.write( "Check: V = A * H = L * W * H = 8 * 6 * 12 = 576
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