document.write( "Question 1022855: Hi, could someone please help with a word problem? The problem is: The hypotenuse of a right triangle is 5 m longer than one leg and 2 m longer than the other leg. Find the perimeter of the right triangle. Thank you! \n" ); document.write( "

Algebra.Com's Answer #638444 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = the length in meters of
\n" ); document.write( "the shorter leg
\n" ); document.write( "Let $\"+b+\"$ = the length in meters of
\n" ); document.write( "the longer leg
\n" ); document.write( "Let $\"+c+\"$ = the length in meters of
\n" ); document.write( "the hypotenuse
\n" ); document.write( "------------------
\n" ); document.write( "(1) $\"+c%5E2+=+a%5E2+%2B+b%5E2+\"$
\n" ); document.write( "(2) $\"+c+=+a+%2B+5+\"$
\n" ); document.write( "(3) $\"+c+=+b+%2B+2+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "(2) $\"+a+=+c+-+5+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+b+=+c+-+2+\"$
\n" ); document.write( "----------------
\n" ); document.write( "Plug (2) and (3) into (1)
\n" ); document.write( "(1) $\"+c%5E2+=+%28+c+-+5+%29%5E2+%2B+%28+c+-+2+%29%5E2+\"$
\n" ); document.write( "(1) $\"+c%5E2+=+c%5E2+-+10c+%2B+25+%2B+c%5E2+-+4c+%2B+4+\"$
\n" ); document.write( "(1) $\"+c%5E2+=+2c%5E2+-+14c+%2B+29+\"$
\n" ); document.write( "(1) $\"+c%5E2+-+14c+%2B+29+=+0+\"$
\n" ); document.write( "Complete the square:
\n" ); document.write( "(1) $\"+c%5E2+-+14c+%2B+%28+14%2F2+%29%5E2++=++-29+%2B+%2814%2F2+%29%5E2+\"$
\n" ); document.write( "(1) $\"+c%5E2+-+14c+%2B+49+=+-29+%2B+49+\"$
\n" ); document.write( "(1) $\"+c%5E2+-+14c+%2B+49+=+20+\"$
\n" ); document.write( "(1) $\"+%28+c+-+7+%29%5E2+=+20+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( "( note that I don't use the negative square root
\n" ); document.write( "since that gives me a negative result for $\"+a+\"$ )\r
\n" ); document.write( "\n" ); document.write( "(1) $\"+c+-+7+=+sqrt%2820%29+\"$
\n" ); document.write( "(1) $\"+c+=+4.472%2B+7+\"$
\n" ); document.write( "(1) $\"+c+=+11.472+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+a+=+c+-+5+\"$
\n" ); document.write( "(2) $\"+a+=+11.472+-+5+\"$
\n" ); document.write( "(2) $\"+a+=+6.472+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+b+=+c+-+2+\"$
\n" ); document.write( "(3) $\"+b+=+11.472+-+2+\"$
\n" ); document.write( "(3) $\"+b+=+9.472+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "The perimeter is:
\n" ); document.write( " $\"+11.472+%2B+6.472+%2B+9.472+=+27.416+\"$
\n" ); document.write( "----------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+c%5E2+=+a%5E2+%2B+b%5E2+\"$
\n" ); document.write( "(1 ) $\"+11.472%5E2++=+6.472%5E2+%2B+9.472%5E2+\"$
\n" ); document.write( "(1) $\"+131.607+=+41.887+%2B+89.719+\"$
\n" ); document.write( "(1) $\"+131.607+=+131.606+\"$
\n" ); document.write( "error due to rounding off
\n" ); document.write( "-----------------------\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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