document.write( "Question 702558: find the area of an isosceles triangle with side lengths 15,15, and 18. \n" ); document.write( "
Algebra.Com's Answer #433041 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "The Problem--\r\n" );
document.write( "Find the area of an isosceles triangle with side lengths 15,15, and 18.\r\n" );
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document.write( "The Solution:\r\n" );
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document.write( "The formula for the area of a triangle is \r\n" );
document.write( "A = (1/2)*B*H\r\n" );
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document.write( "where B is the base and H is the height. The base of this triangle is 18. \r\n" );
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document.write( "Now we need the height.\r\n" );
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document.write( "An isosceles triangle can be split into two congruent right triangles by drawing a line segment\r\n" );
document.write( " from the vertex of the angle across from the base to the base so that the line segment is \r\n" );
document.write( "perpendicular to the base (90 degree angle). The segment cuts the base exactly in half. The \r\n" );
document.write( "length of this segment is the height of the big triangle.\r\n" );
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document.write( "Now you have two right triangles each with hypotenuse of 15 and base 9. (The base of the \r\n" );
document.write( "smaller triangles is 9 because 9 is half of 18.)\r\n" );
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document.write( "Since they are right triangles, we can use the Pythagorean Equation to find the height\r\n" );
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document.write( "a^2 + b^2 = c^2\r\n" );
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document.write( "Let a be the base, a=9.\r\n" );
document.write( "Let b be the height. That's we are trying to find.\r\n" );
document.write( "Let c be the hypotenuse, c=15.\r\n" );
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document.write( "9^2 + b^2 = 15^2\r\n" );
document.write( "81 + b^2 = 225\r\n" );
document.write( "b^2 = 144\r\n" );
document.write( "b = 12\r\n" );
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document.write( "The small triangles have a height of 12. They each have an area of\r\n" );
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document.write( "A = (1/2)*(12)*(9)\r\n" );
document.write( "A = 54\r\n" );
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document.write( "The two small triangles combine to give the area of the large triangle so its area is \r\n" );
document.write( "54+54 = 108.\r\n" );
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document.write( "Best,\r\n" );
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document.write( "Mrs.Figgy\r\n" );
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