document.write( "Question 1190831: the diagonal of a rectangle is 6cm longer than its base. Its height is 10 cm more than one-third of its base. Find the dimension of the resctangle. \n" ); document.write( "

Algebra.Com's Answer #822559 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!


\n" );
document.write( "Let b=base
\n" );
document.write( "Let h=height
\n" );
document.write( "Let d=diagonal\r
\n" );
document.write( "\n" );
document.write( "Given:
\n" );
document.write( "d = b+6
\n" );
document.write( "h = (b/3)+10\r
\n" );
document.write( "\n" );
document.write( "By Pythagorean theorem:
\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "Substitute the givens to get one eqn w/one unknown:
\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "Expand (and cancel one  from each side):
\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "Multiply both sides  by 9:
\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "Bring it all over to one side:
\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "  --->  b = 24  --> h = 18,  d = 30\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Check:
\n" );
document.write( " =  = 900
\n" );
document.write( "  (ok!)\r
\n" );
document.write( "\n" );
document.write( "  \n" );
document.write( "

\n" );