document.write( "Question 94377This question is from textbook Algebra 1
\n" ); document.write( ": The expression 2(l+ w) may be used to find the perimeter of a rectangle. What are the length and width of a rectangle if the area is 13 1/2 square units and the length of one side is 1/5 the measure of the perimeter? \n" ); document.write( "
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The expression 2(l+ w) may be used to find the perimeter of a rectangle. What are the length and width of a rectangle if the area is 13 1/2 square units and the length of one side is 1/5 the measure of the perimeter?
\n" ); document.write( ":
\n" ); document.write( "Using decimal for 1/5. L = .2 * perimeter:
\n" ); document.write( "L = .2(2(L+W))
\n" ); document.write( "L = .4(L+W)
\n" ); document.write( "L = .4L + .4W
\n" ); document.write( "1L - .4L = .4W
\n" ); document.write( ".6L = .4W
\n" ); document.write( ":
\n" ); document.write( "Area is given as 13.5 sq units
\n" ); document.write( "L * W = 13.5
\n" ); document.write( "W = 13.5/L
\n" ); document.write( ":
\n" ); document.write( "Substitute (13.5/L) for W in the .6L = .4W equation
\n" ); document.write( ".6L = .4\"13.5%2FL\"
\n" ); document.write( ".6L = \"5.4%2FL\"
\n" ); document.write( "Multiply equation by L
\n" ); document.write( "\".6L%5E2\" = 5.4
\n" ); document.write( ":
\n" ); document.write( "Divide both sides by .6
\n" ); document.write( "\"L%5E2\" = \"5.4%2F.6\"
\n" ); document.write( ":
\n" ); document.write( "\"L%5E2\" = 9
\n" ); document.write( "L = \"sqrt%289%29\"
\n" ); document.write( "L = 3
\n" ); document.write( ":
\n" ); document.write( "Find W:
\n" ); document.write( "W = 13.5/3
\n" ); document.write( "W = 4.5 units
\n" ); document.write( ":
\n" ); document.write( "Perimeter = 2(3) + 2(4.5) = 15
\n" ); document.write( "Length/Perimeter: 3/15 = 1/5
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