document.write( "Question 1191970: In an isosceles triangle ABC, side AB is twice as long as AC. The perimeter of the triangle is 200cm. Find the length of AC.
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Algebra.Com's Answer #823989 by MathTherapy(10552)\"\" \"About 
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In an isosceles triangle ABC, side AB is twice as long as AC. The perimeter of the triangle is 200cm. Find the length of AC.
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Scenario 1.\r\n" );
document.write( "Let's assume that AC is one of the congruent sides. \r\n" );
document.write( "Then BC is the other congruent side and AB would be the base.\r\n" );
document.write( "Let AC be x. Then BC will also be x, and AB would be 2x.\r\n" );
document.write( "With perimeter being 200 cm, we get: x + x + 2x = 200\r\n" );
document.write( "4x = 200\r\n" );
document.write( "x, or \"matrix%281%2C8%2C+AC%2C+%22=%22%2C+BC%2C+%22=%22%2C+200%2F4%2C+%22=%22%2C+50%2C+cm%29\"\r\n" );
document.write( "Thus, we have the following: AC = 50 cm, BC = 50 cm, and AB = 2(50) = 100 cm.\r\n" );
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document.write( "According to the TRIANGLE INEQUALITY, the 3rd side of ANY TRIANGLE, MUST be GREATER than the DIFFERENCE of the other 2 sides,\r\n" );
document.write( "but less than their SUM. In this case, it would be: (50 - 50) < 3rd side < (50 + 50), which results in:  \r\n" );
document.write( "0 < 100 < 100, which is FALSE.\r\n" );
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document.write( "Scenario 2.\r\n" );
document.write( "We now make the longer sides congruent\r\n" );
document.write( "Then the base, AC would be the shortest side\r\n" );
document.write( "Let AC be x. \r\n" );
document.write( "Then AB and BC would be 2x, each.\r\n" );
document.write( "With perimeter being 200 cm, we get: x + 2x + 2x = 200\r\n" );
document.write( "5x = 200\r\n" );
document.write( "x, or \"matrix%281%2C6%2C+ABC%2C+%22=%22%2C+200%2F5%2C+%22=%22%2C+40%2C+cm%29\"\r\n" );
document.write( "Thus, we have the following: AC = 40 cm, AB = BC = 2(40) = 80 cm.\r\n" );
document.write( "\r\n" );
document.write( "According to the TRIANGLE INEQUALITY, the 3rd side of ANY TRIANGLE, MUST be GREATER than the DIFFERENCE of the other 2 sides,\r\n" );
document.write( "but less than their SUM. In this case, it would be: (80 - 80) < 3rd side < (80 + 80), which results in:  \r\n" );
document.write( "0 < 40 < 160, which is TRUE.\r\n" );
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document.write( "Therefore, AC's length is: 40 cm.
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