document.write( "Question 446949: If we are given that the distance around a piece of property is 30 miles what would be the range of possible areas that the property could have- now also given that the shape is a rectangle what would be the possible areas that the property could have \n" ); document.write( "

Algebra.Com's Answer #307768 by htmentor(1343) $\"\"$ $\"About$

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If the property has a rectangular shape then for the perimeter and area we can write:
\n" ); document.write( "2l + 2w = 30 -> l + w = 15
\n" ); document.write( "l*w = A
\n" ); document.write( "where l=length, w=width
\n" ); document.write( "We can express w in terms of l:
\n" ); document.write( "w = 15 - l
\n" ); document.write( "Then A = l(15 - l)
\n" ); document.write( "We assume that the lengths of the sides are made up of whole numbers.
\n" ); document.write( "The range of areas will be obtained if we let l range from 1 to 7.
\n" ); document.write( "Note that we can stop at 7 since 8*7 = 7*8, 9*6 = 6*9, etc.
\n" ); document.write( "For l = 1, A = (1)(14) = 14
\n" ); document.write( "For l = 7, A = (7)(8) = 56
\n" ); document.write( "So the range of areas is 14 to 56 sq. mi.
\n" ); document.write( "The graph of the area as a function of the length is shown below.
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-70%2C70%2Cx%2A%2815-x%29%29\"$
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