document.write( "Question 1092306: Liboko builds a rectangular storeroom. If the diagonal of the room is √1312 m and the perimeter is 80 m , determine the dimensions of the room. \n" ); document.write( "

Algebra.Com's Answer #706908 by greenestamps(13334) $\"\"$ $\"About$

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Let x and y be the length and width of the room.

\n" ); document.write( "The perimeter is 80:
\n" ); document.write( " $\"2x%2B2y+=+80\"$
\n" ); document.write( " $\"x%2By+=+40\"$ (1)

\n" ); document.write( "The diagonal of the room is the square root of 1312:
\n" ); document.write( " $\"sqrt%28x%5E2%2By%5E2%29+=+sqrt%281312%29\"$
\n" ); document.write( " $\"x%5E2%2By%5E2+=+1312\"$ (2)

\n" ); document.write( "To solve the system of equations (1) and (2), first square (1):
\n" ); document.write( " $\"x%5E2+%2B+2xy+%2B+y%5E2+=+1600\"$ (3)

\n" ); document.write( "Then subtract (2) from (3):
\n" ); document.write( " $\"2xy+=+288\"$
\n" ); document.write( " $\"xy+=+144\"$ (4)

\n" ); document.write( "You could solve (1) and (4) algebraically; but it's faster just to look for a pair of numbers whose sum is 40 and whose product is 144. Those numbers are 36 and 4.

\n" ); document.write( "Liboko has a very long and narrow storeroom with length 36m and width 4m. \n" ); document.write( "

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