document.write( "Question 166988This question is from textbook Introductory Algebra
\n" ); document.write( ": The mainsail of a Lightning sailboat is a right triangle in which the hypotenuse is called the leech. If a 24-ft tall mainsail has a leech length of 26 ft and if sailcloth costs $10 per square foot, find the cost of a new mainsail. \n" ); document.write( "
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The mainsail of a Lightning sailboat is a right triangle in which the hypotenuse is called the leech. If a 24-ft tall mainsail has a leech length of 26 ft and if sailcloth costs $10 per square foot, find the cost of a new mainsail.
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\n" ); document.write( "Let x = base of right triangle
\n" ); document.write( "then applying Pythagorean theorem:
\n" ); document.write( "x^2 + 24^2 = 26^2
\n" ); document.write( "x^2 + 576 = 676
\n" ); document.write( "x^2 = 100
\n" ); document.write( "x = {-10, +10}
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\n" ); document.write( "We can toss out the negative solution leaving us with
\n" ); document.write( "base = 10 ft
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\n" ); document.write( "Area of sail = (1/2)bh
\n" ); document.write( "Area of sail = (1/2)(10)(24)
\n" ); document.write( "Area of sail = (5)(24)
\n" ); document.write( "Area of sail = 120 sq ft
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\n" ); document.write( "Finally, if it is $10 per sq ft:
\n" ); document.write( "10 * 120 = $1200 (cost of new mainsail)\r
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