document.write( "Question 198521: The altitude of a triangle is 3/4 the length of its base. If the altitude were increased by 3 feet and the base decreased by 3 feet, the area would be unchanged. Find the length of the base and altitude. \n" ); document.write( "
Algebra.Com's Answer #149043 by nerdybill(7384)\"\" \"About 
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The altitude of a triangle is 3/4 the length of its base. If the altitude were increased by 3 feet and the base decreased by 3 feet, the area would be unchanged. Find the length of the base and altitude.
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\n" ); document.write( "Original triangle:
\n" ); document.write( "Let b = length of base
\n" ); document.write( "then
\n" ); document.write( "(3/4)b = altitude
\n" ); document.write( "Area = (1/2)b(3/4)b = (3/8)b^2
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\n" ); document.write( "Changed triangle:
\n" ); document.write( "b-3 = length of base
\n" ); document.write( "(3/4)b+3 = altitude
\n" ); document.write( "Area = (1/2)(b-3)(3/4)b+3 = (3/8)(b-3)b+3
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\n" ); document.write( "Set area equal to each other:
\n" ); document.write( "(3/8)b^2 = (3/8)(b-3)b+3
\n" ); document.write( "b^2 = (b-3)b+3
\n" ); document.write( "b^2 = b^2-3b+3
\n" ); document.write( "0 = -3b+3
\n" ); document.write( "-3 = -3b
\n" ); document.write( "1 feet = b (base of triangle)
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\n" ); document.write( "Altitude:
\n" ); document.write( "(3/4)b = (3/4)1 = 3/4 feet (altitude)\r
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