document.write( "Question 1132035: Land in the shape of an isosceles triangle has a base of 130 m. An altitude from one of the legs of the triangle is 120 m. What is the area of the property?
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\n" ); document.write( "Can someone please solve this without using trignometry.
\n" ); document.write( "a) 3000
\n" ); document.write( "b) 9840
\n" ); document.write( "c) 9512
\n" ); document.write( "d) 10 140
\n" ); document.write( "e) 10 200 \n" ); document.write( "

Algebra.Com's Answer #748877 by ikleyn(52838) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let the triangle be ABC with the base AB and the lateral sides AC and BC.\r\n" );
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document.write( "Let AD be the altitude of the triangle drawn from A to the lateral side BC.\r\n" );
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document.write( "Then DC is the leg in the right angle triangle ADB with the hypotenuse AB= 130 m and the other leg AD = 120 m - hence\r\n" );
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document.write( "    |DB| =  = 50 m.\r\n" );
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document.write( "Draw the altitude CE from vertex C to the base AB.\r\n" );
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document.write( "The triangles ADB and CEB are similar (since they are right-angled triangles with the common acute angle B). Hence,\r\n" );
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document.write( "     = ,  or   = ,\r\n" );
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document.write( "where  h is the altitude CE:  h = |CE|.  It gives for h\r\n" );
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document.write( "    h =  = 12*13  meters.\r\n" );
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document.write( "Now the area of the triangle  ABC  is   \r\n" );
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document.write( "    Area =  = 130*6*13 = 10140 square meters.    ANSWER\r\n" );
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