document.write( "Question 1164867: Rectangle ABCD has sides AB = 21 and AD = 28. Let P be a point
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Algebra.Com's Answer #789333 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "1.  Make a sketch.\r\n" );
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document.write( "    In the sketch, draw the perpendicular from the point P to the side AB of the rectangle.\r\n" );
document.write( "    Let E be the foot of this perpendicular at AB.\r\n" );
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document.write( "    In the sketch, draw the perpendicular from the point P to the side AD of the rectangle.\r\n" );
document.write( "    Let F be the foot of this perpendicular at AD.\r\n" );
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document.write( "2.  Using the Heron's formula, find the area S of the triangle APB.  It is\r\n" );
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document.write( "        area S =  =  = 84.\r\n" );
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document.write( "    Here in the formula  24 =   is the semi-perimeter of the triangle APB.\r\n" );
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document.write( "3.  By knowing the area of the triangle APB (84 square units) and its base AB (21 units), \r\n" );
document.write( "    you can find its altitude, which is  = 8 units.\r\n" );
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document.write( "4.  Now in the right angled triangle APE, you know its hypotenuse AP = 17  and one of the legs PE = 8.\r\n" );
document.write( "    Hence, the other leg is   = 15 units.\r\n" );
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document.write( "5.  So, you know now the lengths of both perpendiculars  PE and PF, i.e. distances of the point P from \r\n" );
document.write( "    two sides of the rectangle.\r\n" );
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document.write( "6.  The rest of the solution is easy, and I leave it to you to complete it on your own.\r\n" );
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document.write( "ANSWER.  PD = 25; PC =  = .\r\n" );
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