document.write( "Question 884649: A carpenter is making a backyard deck. In his measurements, he has determined that he needs to make a support triangle with an area 22 mē. He knows that the base must be 1 less than 3 times the height. If the base is represented by 3x - 1 and the height = x, find the dimensions of the triangle. \n" ); document.write( "
Algebra.Com's Answer #534561 by nerdybill(7384)\"\" \"About 
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A carpenter is making a backyard deck. In his measurements, he has determined that he needs to make a support triangle with an area 22 mē. He knows that the base must be 1 less than 3 times the height. If the base is represented by 3x - 1 and the height = x, find the dimensions of the triangle.
\n" ); document.write( "base = 3x - 1
\n" ); document.write( "height = x
\n" ); document.write( "area of triangle = (1/2)bh
\n" ); document.write( "22 = (1/2)(3x-1)(x)
\n" ); document.write( "44 = (3x-1)(x)
\n" ); document.write( "44 = 3x^2-x
\n" ); document.write( "0 = 3x^2-x-44
\n" ); document.write( "0 = 3x^2-12x+11x-44
\n" ); document.write( "0 = (3x^2-12x)+(11x-44)
\n" ); document.write( "0 = 3x(x-4)+11(x-4)
\n" ); document.write( "0 = (x-4)(3x+11)
\n" ); document.write( "x = {-11/3, 4}
\n" ); document.write( "throw out the negative solution (extraneous) leaving
\n" ); document.write( "x = 4 m (height)
\n" ); document.write( ".
\n" ); document.write( "Base:
\n" ); document.write( "3x - 1 = 3(4) - 1 = 12 - 1 = 11 m (base)\r
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