document.write( "Question 827647: Please help me solving this question \"A footpath a uniform width runs round the inside of a rectangle field 32m long and 24 m wide,if path occupies 208sq.m,find the width of the footpath. \" \n" ); document.write( "
Algebra.Com's Answer #498803 by rothauserc(4718)\"\" \"About 
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let x be the width of the footpath and we want to subtract the areas of two rectangles
\n" ); document.write( "208 = (32*24) - ((32-2x)*(24-2x))
\n" ); document.write( "208 = 768 - (768 -112x +4x^2)
\n" ); document.write( "208 = 112x -4x^2
\n" ); document.write( "4x^2 -112x +208 = 0
\n" ); document.write( "divide both sides of = by 4
\n" ); document.write( "x^2 -28x +52 = 0
\n" ); document.write( "this expression factors into
\n" ); document.write( "(x-2) * (x-26) = 0
\n" ); document.write( "we have two solutions for x, namely 2 and 26 BUT we can eliminate 26 since that value is greater than the width of the larger rectangle, now check the answer
\n" ); document.write( "x = 2 m
\n" ); document.write( "208 = 768 - (28 * 20)
\n" ); document.write( "208 = 768 - 560
\n" ); document.write( "208 = 208
\n" ); document.write( "answer checks\r
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