document.write( "Question 1207920: A garden 7 m by 12 m will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an area of 92 im \n" ); document.write( "

Algebra.Com's Answer #846067 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The other tutor showed a typical formal algebraic solution.

\n" ); document.write( "If formal algebra is not required, and if the speed of obtaining the answer is important -- as on a timed competitive exam -- then the problem can be solved easily and quickly with logical reasoning and a little mental arithmetic.

\n" ); document.write( "The area of the original garden is 7*12 = 84 square meters; with the added border of flowers of uniform width, the area is 84+92 = 176 square meters.

\n" ); document.write( "The difference between the width and length is 5 meters; since the border of flowers is of uniform width, the difference between the length and width of the expanded garden is again 5 meters.

\n" ); document.write( "So to find the solution, you need only find two numbers that differ by 5 and have a product of 176. A bit of playing with numbers shows those two numbers to be 11 and 16.

\n" ); document.write( "The garden without the border is 7 by 12 meters; with the border it is 11 by 16 meters. Since the border is uniform width on all four sides, the width of the border is 2 meters.

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