document.write( "Question 40299: Q1) PQRS is a rectangle in which PQ = 9 cm and PS = 6 cm. T is a point on PQ such that PT = 7 cm and RV is the perpendicular from R to ST. Calculate ST and RV. \r
\n" ); document.write( "\n" ); document.write( "I managed to calculate ST but not RV. \r
\n" ); document.write( "\n" ); document.write( "Q2) In a pararllelogram ABCD, the diagonal AC is at right angles to AB. If AB = 12 cm and BC = 13 cm, find the area of the parallelogram.\r
\n" ); document.write( "\n" ); document.write( "Please advise and hope you can assist me to solve these questions. Thank you very much.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #25673 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Q1) PQRS is a rectangle in which PQ = 9 cm and PS = 6 cm. \r\n" );
document.write( "T is a point on PQ such that PT = 7 cm and RV is\r\n" );
document.write( "the perpendicular from R to ST. Calculate ST and\r\n" );
document.write( "RV. \r\n" );
document.write( "\r\n" );
document.write( "I managed to calculate ST but not RV.\r\n" );
document.write( "                       _____    _____    __\r\n" );
document.write( "I assume you got ST = ﾖ6ｲ+7ｲ = ﾖ36+49 = ﾖ85\r\n" );
document.write( "\r\n" );
document.write( "By alternate interior angles, ﾐRSV = ﾐPTS\r\n" );
document.write( "    \r\n" );
document.write( "Right triangles RVS and SPT are similar, since two \r\n" );
document.write( "triangles are similar if 2 angles of one triangle \r\n" );
document.write( "have the same measures as 2 angles of the other,\r\n" );
document.write( "and we know that both contain a right angle.\r\n" );
document.write( "\r\n" );
document.write( "Therefore\r\n" );
document.write( "\r\n" );
document.write( " RV     RS \r\n" );
document.write( "覧覧 = 覧覧\r\n" );
document.write( " PS     ST\r\n" );
document.write( "\r\n" );
document.write( " RV      9 \r\n" );
document.write( "覧覧 = 覧覧予r\n" );
document.write( " 6      ﾖ85\r\n" );
document.write( "     __\r\n" );
document.write( " RVﾗﾖ85 = 9ﾗ6\r\n" );
document.write( "     __\r\n" );
document.write( " RVﾗﾖ85 = 54\r\n" );
document.write( "          __\r\n" );
document.write( " RV = 54/ﾖ85 cm exactly or about 5.86 cm\r\n" );
document.write( "\r\n" );
document.write( "Q2) In a pararllelogram ABCD, the diagonal AC is at\r\n" );
document.write( "right angles to AB. If AB = 12 cm and BC = 13 cm, \r\n" );
document.write( "find the area of the parallelogram.\r\n" );
document.write( "\r\n" );
document.write( "D_____C\r\n" );
document.write( " \   |\\r\n" );
document.write( "  \  | \13\r\n" );
document.write( "   \ |  \\r\n" );
document.write( "    \|___\\r\n" );
document.write( "    A  12 B\r\n" );
document.write( "\r\n" );
document.write( "That figure is not to scale, as it should be leaning \r\n" );
document.write( "farther to the left, but it will do for our purpose.\r\n" );
document.write( "\r\n" );
document.write( "Area of parallelogram = base ﾗ height =\r\n" );
document.write( "\r\n" );
document.write( "                            AB ﾗ AC = 12 ﾗ AC\r\n" );
document.write( "\r\n" );
document.write( "We find AC by the Pythagorean theorem\r\n" );
document.write( "      _________    _________    __\r\n" );
document.write( "AC = ﾖ13ｲ + 12ｲ = ﾖ169 - 144 = ﾖ25 = 5\r\n" );
document.write( "\r\n" );
document.write( "So area of parallelogram = 12 ﾗ AC = 12 ﾗ 5 = 60 cmｲ\r\n" );
document.write( "\r\n" );
document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

\n" ); document.write( " \n" ); document.write( "
\n" );