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area of a rectangle is 243 square inches.
\n" ); document.write( "the formula for area is length * width which can also be expressed as base * height.
\n" ); document.write( "we have b * h = a1
\n" ); document.write( "we have 1/3 * b * 2 * h = a2
\n" ); document.write( "this simplifies to:
\n" ); document.write( "2/3 * b * h = a2
\n" ); document.write( "the ratio of a2 / a1 is equivalent to:
\n" ); document.write( "(2/3 * b * h) / (b * h)
\n" ); document.write( "Since b*h in the numberator and b*h in the denominator cancel out, then the resulting ratio of a2 / a1 is equal to 2/3
\n" ); document.write( "this means that a2 is equal to 2/3 * a1
\n" ); document.write( "since a1 = b * h and b * h = 243, this means that the new area is equal to 2/3 * 243 which make it equal to 162 square inches.
\n" ); document.write( "it shouldn't really matter what b is and what h is.
\n" ); document.write( "example:
\n" ); document.write( "assume b = 10 inches.
\n" ); document.write( "this means that h = 243/10 = 24.3 inches.
\n" ); document.write( "the area is 10 * 24.3 = 243 square inches.
\n" ); document.write( "now we take 1/3 * the base to get 1/3 * 10 = 3.33333333 inches
\n" ); document.write( "we take 2 times the height to get 48.6 inches.
\n" ); document.write( "3.33333333 * 48.6 = 162 square inches.
\n" ); document.write( "assume b = 20 inches.
\n" ); document.write( "this means that h = 243/20 = 12.15 inches.
\n" ); document.write( "20 * 12.15 = 243 square inches.
\n" ); document.write( "1/3 * 20 = 6.6666667 inches.
\n" ); document.write( "12.15 * 2 = 24.3 inches.
\n" ); document.write( "6.6666667 * 24.3 inches = 162 square inches.
\n" ); document.write( "everything checks out.
\n" ); document.write( "the new area would be 162 square inches.
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