document.write( "Question 888596: a rectangle has perimeter 62 and area 136. what is the length of the rectangle's diagonal? \n" ); document.write( "

Algebra.Com's Answer #537493 by lwsshak3(11628) $\"\"$ $\"About$

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a rectangle has perimeter 62 and area 136. what is the length of the rectangle's diagonal?
\n" ); document.write( "***
\n" ); document.write( "let x=length of rectangle
\n" ); document.write( "let y=width of rectangle
\n" ); document.write( "2x+2y=perimeter=62
\n" ); document.write( "2y=62-2x
\n" ); document.write( "y=(62-2x)/2=31-x
\n" ); document.write( "length*width=area
\n" ); document.write( "x*y=136
\n" ); document.write( "x(31-x)=136
\n" ); document.write( "31x-x^2=136
\n" ); document.write( "x^2-31x+136
\n" ); document.write( "solve by quadratic formula:
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "a=1, b=-31, c=36
\n" ); document.write( "ans:
\n" ); document.write( "x=1.14 (reject)
\n" ); document.write( "or
\n" ); document.write( "x=29.36
\n" ); document.write( "y=62-2x=3.28
\n" ); document.write( "By the pythagorean theorem:
\n" ); document.write( "√(x^2+y^2)=diagonal
\n" ); document.write( "√(29.36^2+3.28^2)=√872.77
\n" ); document.write( "diagonal=29.54
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