document.write( "Question 185893This question is from textbook Beginning Algebra
\n" ); document.write( ": would you please help me with this problem, i have been racking my brain for two days to figure it out...ok this is how it goes: There is a sailboat which must have a 110 ft mast and a combined mainsain and jibsail area of 3000 sq ft. The design calls for the mainsail to be 60% of the combined sail area,and the jibsail area to be 40%(of course). If the height of the triangular mainsail is 28ft more than twice the length of the boom, find the length of the boom and the height of the mainsail. \r
\n" ); document.write( "\n" ); document.write( "I've figured out this much so far... the mainsail=1800sq ft, and the jibsail =1200sq ft. Height=(2(boom)+28sq ft). and i know that the area of a triangle is A=1/2(base)(heigth). that is about it, i've played around with the numbers but haven't gotten it correct yet. Any help you can offer would be tramendous!Thanks \n" ); document.write( "
Algebra.Com's Answer #139417 by ankor@dixie-net.com(22740)\"\" \"About 
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There is a sailboat which must have a 110 ft mast and a combined mainsail and jib-sail area of 3000 sq ft. The design calls for the mainsail to be 60% of the combined sail area,and the jib-sail area to be 40%(of course). If the height of the triangular mainsail is 28ft more than twice the length of the boom, find the length of the boom and the height of the mainsail.
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\n" ); document.write( "We can determine that the mainsail area must be .6*3000 = 1800 sq/ft
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\n" ); document.write( "Assume the mailsail is a right triangle,
\n" ); document.write( "let x = the length of the boom\
\n" ); document.write( "then
\n" ); document.write( "(2x+28) = the height of the mainsail
\n" ); document.write( "we have the area equation:
\n" ); document.write( ".5 * x * (2x+28) = 1800
\n" ); document.write( ".5x(2x+28) = 1800
\n" ); document.write( "1x^2 + 14x = 1800
\n" ); document.write( "a quadratic equation:
\n" ); document.write( "x^2 + 14x - 1800 = 0
\n" ); document.write( "Factor this to
\n" ); document.write( "(x+50)(x-36) = 0
\n" ); document.write( "positive solution:
\n" ); document.write( "x = 36' is the boom
\n" ); document.write( "and the height of the mainsail
\n" ); document.write( "2(36) + 28 = 100'
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\n" ); document.write( "Check the area:
\n" ); document.write( ".5*36*100 = 1800 sq/ft\r
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