document.write( "Question 1132689: ABCD and IJKL are squares where measures shown for side AE and side DE apply to the other three sides of ABCD. Find the area of square IJKL in cm^2.
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Algebra.Com's Answer #749805 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The side length of the larger square is (6+12) = 18 centimeters, so its area is   = 324 cm^2.\r\n" );
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document.write( "Now, there are 4 congruent right angled triangles  ALD,  DKC, CBJ  and  BIA.\r\n" );
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document.write( "The area of the smaller square is 324 cm^2  MINUS  4 times the area of the triangle ALD.\r\n" );
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document.write( "Triangle ALD is similar to triangle ADH (they both are right angled triangles and have common acute angle DAL).\r\n" );
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document.write( "Triangle ALD has the hypotenuse  AD = 6+12 = 18 cm.\r\n" );
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document.write( "Triangle ADH has the hypotenuse  AH =  =  = .\r\n" );
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document.write( "The ratio of the hypotenuses  |AH|/|AD| =  =   (the similarity coefficient).\r\n" );
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document.write( "Hence, the ratio of the areas of the triangles  ADH  and  ALD  is the square of the similarity coefficient, i.e.  .\r\n" );
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document.write( "The area of the triangle  ADH  is   = 54 cm^2.\r\n" );
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document.write( "Hence, the area of the triangle  ALD  is   cm^2 = 48.6 cm^2.\r\n" );
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document.write( "Then the area of the smaller square is (as I explained it above)  324 - 4*48.6 = 129.6 cm^2.      ANSWER\r\n" );
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