document.write( "Question 1014172: A field in the from of a parallelogram has an area of 432 m2 find the length of its diagonal on which the perpendiculars drawn from two vertices on either side of it are 12m long. \n" ); document.write( "

Algebra.Com's Answer #630520 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A field in the from of a parallelogram has an area of 432 m2 find the length of its diagonal on which the perpendiculars drawn from two vertices on either side of it are 12m long.
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document.write( "Make a sketch. Draw the diagonal and two perpendiculars from the vertices of the parallelogram to this diagonal. \r\n" );
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document.write( "The diagonal divides the parallelogram in two congruent triangles.\r\n" );
document.write( "Do you know it? If not, look into the lesson In a parallelogram, each diagonal divides it in two congruent triangles in this site. \r\n" );
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document.write( "Notice, that perpendiculars drown to the diagonal are altitudes in the triangles.\r\n" );
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document.write( "Now, the area of each of these two triangles is half of the product of the diagonal measure and the altitude, \r\n" );
document.write( "i.e. , where x is the unknown length of the diagonal.\r\n" );
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document.write( "The sum of these areas is the area of the parallelogram, which is given.\r\n" );
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document.write( "So, you have this equation to find the length of the diagonal:\r\n" );
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document.write( "12*x = 432.\r\n" );
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document.write( "Hence, x =  = 36 m.\r\n" );
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document.write( "Answer. The length of the diagonal is 36 m.\r\n" );
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