document.write( "Question 1165102: An isosceles trapezium ABCD has perpendicular diagonals and side lengths
\n" ); document.write( "AB = 1 and CD = 7.
\n" ); document.write( "(a) Find the length of the two equal sides.
\n" ); document.write( "(b) Find the product of the lengths of the diagonals. \n" ); document.write( "
Algebra.Com's Answer #789574 by Edwin McCravy(20067)\"\" \"About 
You can put this solution on YOUR website!
An isosceles trapezium ABCD has perpendicular diagonals and side lengths
\n" ); document.write( "AB = 1 and CD = 7.
\n" ); document.write( "(a) Find the length of the two equal sides.
\n" ); document.write( "
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document.write( "Triangles ABE and CDE are similar right triangles, so\r\n" );
document.write( "\"a%2F7=b%2F1\"\r\n" );
document.write( "\"a=7b\"\r\n" );
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document.write( "The diagonals are perpendicular so we can use the Pythagorean theorem\r\n" );
document.write( "on the right triangles.\r\n" );
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document.write( "\"b%5E2%2Bb%5E2=1%5E2\"\r\n" );
document.write( "\"2b%5E2=1\"\r\n" );
document.write( "\"b%5E2=1%2F2\"\r\n" );
document.write( "\"b=sqrt%281%2F2%29\"\r\n" );
document.write( "\"b=1%2Fsqrt%282%29\"\r\n" );
document.write( "\"b=sqrt%282%29%2F2\"\r\n" );
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document.write( "\"a=7b=7sqrt%282%29%2F2\"\r\n" );
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document.write( "\"BC%5E2=a%5E2%2Bb%5E2\"\r\n" );
document.write( "\"BC%5E2=%287sqrt%282%29%2F2%29%5E2%2B%28sqrt%282%29%2F2%29%5E2\"\r\n" );
document.write( "\"BC%5E2=%2849%2A2%29%2F4%2B2%2F4\"\r\n" );
document.write( "\"BC%5E2=98%2F4%2B2%2F4\"\r\n" );
document.write( "\"BC%5E2=100%2F4\"\r\n" );
document.write( "\"BC%5E2=25\"\r\n" );
document.write( "\"BC=5\"\r\n" );
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document.write( "So the two equal sides are 5 each.

\n" ); document.write( "(b) Find the product of the lengths of the diagonals.
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document.write( "The two diagonals are equal, and they are a+b each\r\n" );
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document.write( "\"a%2Bb=sqrt%282%29%2F2%2B7sqrt%282%29%2F2=8sqrt%282%29%2F2=4sqrt%282%29\"\r\n" );
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document.write( "Multiply them together, which means to square that:\r\n" );
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document.write( "\"%284sqrt%282%29%29%5E2=16%2A2=32\"\r\n" );
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document.write( "That's the product of the diagonals.\r\n" );
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document.write( "Edwin
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