document.write( "Question 90350This question is from textbook algebra and trigonometry
\n" ); document.write( ": please help me with this following polynomial equation word problem and please show work so i know and understand how to do it. \r
\n" ); document.write( "\n" ); document.write( "The area of a right triangle is 250 in^2. Find the lengths of its leg if one of the leg is 5 inches longer then the other. (use the five step method.)
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Algebra.Com's Answer #65564 by Earlsdon(6294)\"\" \"About 
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Find the length of the legs of a right triangle if the area is 250 sq.in. and one leg is 5\" more than the other leg.
\n" ); document.write( "Starting with the formula for the area of a triangle: \"A+=+bh%2F2\"
\n" ); document.write( "A = 250 sq.in.
\n" ); document.write( "let b = x, then h = x+5, so...
\n" ); document.write( "\"250+=+x%28x%2B5%29%2F2\" Multiply both sides by 2.
\n" ); document.write( "\"500+=+x%28x%2B5%29\" Perform the indicated multiplication on the right side.
\n" ); document.write( "\"500+=+x%5E2%2B5x\" Put this into the standard form for quadratic equations (\"ax%5E2%2Bbx%2Bc+=+0\") by subtracting 500 from both sides.
\n" ); document.write( "\"x%5E2%2B5x-500+=+0\" Factor this trinomial.
\n" ); document.write( "\"%28x%2B25%29%28x-20%29+=+0\" Apply the zero products principle.
\n" ); document.write( "\"x%2B25+=+0\" or \"x-20+=+0\"
\n" ); document.write( "\"x+=+-25\" or \"x+=+20\" Discard the negative solution as side lengths are positive.
\n" ); document.write( "\"x+=+20\"inches, and...
\n" ); document.write( "\"x%2B5+=+25\"inches.
\n" ); document.write( "The legs are: 20 inches and 25 inches.\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "\"A+=+%2820%29%2825%29%2F2\"
\n" ); document.write( "\"A+=+500%2F2\"
\n" ); document.write( "\"A+=+250\"sq.in.
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