document.write( "Question 198416: In rectangle ABCD, AB=6 and the length of diagonal AC is 10. The area of ABCD is
\n" ); document.write( "1.60
\n" ); document.write( "2.48
\n" ); document.write( "3.32
\n" ); document.write( "4.28 \n" ); document.write( "
Algebra.Com's Answer #149055 by anantha(86)\"\" \"About 
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sol:
\n" ); document.write( "in rectangle ABCD in which AC and BD are diagonals
\n" ); document.write( "then AC^2+BD^2=AB^2+BC^2+CD^2+DA^2
\n" ); document.write( "PROOF:
\n" ); document.write( "IN RIGHT ANGLED TRIANGLE ABC
\n" ); document.write( "AC^2=AB^2+BC^2 (PYTHAGORAS THEOREM)
\n" ); document.write( "IN RIGHT ANGLED TRIANGLEBDC
\n" ); document.write( "BD^2=BC^2+CD^2
\n" ); document.write( "ADDING ABOVE EQUATIONS
\n" ); document.write( "AC^2+BD^2=AB^2+BC^2+BC^2+CD^2
\n" ); document.write( "AC^2+BD=AB^2+BC^2+DA^2+CD^2 (BC=DA)
\n" ); document.write( "in rectangle AB=DC=6 given,AD=BC=x taken,AC=BD=10 GIVEN
\n" ); document.write( "substitute these values in the above formula
\n" ); document.write( "10^2+10^2=6^2+x^2+x^2+6^2
\n" ); document.write( "100+100=36+x^2+x^2+36
\n" ); document.write( "200=72+2x^2
\n" ); document.write( "2x^2=200-72
\n" ); document.write( "2x^2=128
\n" ); document.write( "x^2=64
\n" ); document.write( "x=sqrt(64)=8
\n" ); document.write( "AB=6 AND BC=8
\n" ); document.write( "Area of the rectangle=AB*BC=6*8=48 \n" ); document.write( "
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