document.write( "Question 742336: A rectangular corner lot has sidewalks on two adjacent sides for a total length of 89 feet. If the diagonal path across the lot is 64 feet, what is the length of the two sides of the walk? Round your answer to two decimal places. \n" ); document.write( "

Algebra.Com's Answer #452477 by KMST(5328) $\"\"$ $\"About$

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Not knowing the width of the sidewalk, we have to assume that the 89 feet of sidewalk were measured along edge of the sidewalk that is also the edge of the lot.
\n" ); document.write( " $\"x\"$ = length of one edge of the lot, in feet
\n" ); document.write( " $\"y\"$ = length of the other edge of the lot, in feet
\n" ); document.write( "The total length of those two edges that are also the edge of the sidewalk is
\n" ); document.write( " $\"x%2By=89\"$ <--> $\"y=89-x\"$
\n" ); document.write( "the diagonal path across the lot divides the lot into two congruent right triangles. That diagonal path is the hypotenuse of those triangles. The edges of the lot are the legs of those right triangles.
\n" ); document.write( "Applying Pythagoras, we get
\n" ); document.write( " $\"x%5E2%2By%5E2=64%5E2\"$ --> $\"x%5E2%2By%5E2=4096\"$
\n" ); document.write( "Substituting $\"y=89-x\"$ we get
\n" ); document.write( " $\"x%5E2%2B%2889%5E2-178x%2Bx%5E2%29%5E2=4096\"$ --> $\"2x%5E2-178x%2B7921=4096\"$ --> $\"2x%5E2-178x%2B3825=0\"$
\n" ); document.write( "We solve that quadratic equation using the quadratic formula:
\n" ); document.write( "

\n" ); document.write( "That gives us two solutions:
\n" ); document.write( " $\"x=%2889%2Bsqrt%28271%29%29%2F2=52.73\"$ (rounded) and $\"x=%2889-sqrt%28271%29%29%2F2=36.27\"$
\n" ); document.write( "Either value could be $\"x\"$ , but then the other one would be $\"y\"$ ,
\n" ); document.write( "So the lot measures $\"highlight%2852.73ft%29\"$ by $\"highlight%2836.27ft%29\"$ . \n" ); document.write( "

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