document.write( "Question 200681: Please I need help with this. Find x if shaded area is 90.the (whole rectangle is shaded except for the holes) By developing and solving by factoring quadratic equation. The rectangle width is 2x-2, length is 3x, and there are 3 holes cut out with the width of x and length of x-1. I know l*w=A but how do you take out the hole squares? \n" ); document.write( "
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Please I need help with this. Find x if shaded area is 90.the (whole rectangle is shaded except for the holes) By developing and solving by factoring quadratic equation. The rectangle width is 2x-2, length is 3x, and there are 3 holes cut out with the width of x and length of x-1. I know l*w=A but how do you take out the hole squares?
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\n" ); document.write( "Area of rectangle = (3x)(2x-2)
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\n" ); document.write( "Area of one hole = x(x-1)
\n" ); document.write( "Three holes would then be 3x(x-1)
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\n" ); document.write( "\"Shaded area\" = \"area of rectangle\" - \"area of holes\"
\n" ); document.write( "90 = (3x)(2x-2) - 3x(x-1)
\n" ); document.write( "On the right side, distribute:
\n" ); document.write( "90 = (6x^2-6x) - (3x^2-3x)
\n" ); document.write( "90 = 6x^2-6x - 3x^2+3x
\n" ); document.write( "90 = 3x^2-3x
\n" ); document.write( "0 = 3x^2-3x-90
\n" ); document.write( "0 = x^2-x-30
\n" ); document.write( "Factoring:
\n" ); document.write( "0 = (x-6)(x+5)
\n" ); document.write( "x = {-5, 6}
\n" ); document.write( "Throwing out the negative solution we get:
\n" ); document.write( "x = 6
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