document.write( "Question 64167: In right triangle ACB (C is the right angle) CD is an altitude (D is between A and B). If AD=x^2 and BD=y^2, use Geometric Mean Theorems to find AC, BC, and CD interms of x and y (assume that x and y are positive) \n" ); document.write( "
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In right triangle ACB (C is the right angle) CD is an altitude (D is between A and B). If AD=x^2 and BD=y^2, use Geometric Mean Theorems to find AC, BC, and CD interms of x and y (assume that x and y are positive)
\n" ); document.write( "FROM SIMILAR TRIANGLES ACB,ADC,CDB,WE GET
\n" ); document.write( "AC/AD=AB/AC....OR......AC^2 = AD*AB....................1
\n" ); document.write( "CB/DB=AB/CB....OR......CB^2 = AB*DB.......................2
\n" ); document.write( "DC/DB=AD/CD....OR.......CD^2 = AD.DB.....................3
\n" ); document.write( "FROM EQN.3
\n" ); document.write( "CD^2=X^2*Y^2
\n" ); document.write( "CD=XY...............4
\n" ); document.write( "FROM EQN.1
\n" ); document.write( "AC^2=X^2(AD+DB)=X^2(X^2+Y^2)
\n" ); document.write( "AC = X*SQRT(X^2+Y^2)
\n" ); document.write( "FROM EQN.2
\n" ); document.write( "CB^2=(AD+DB)*Y^2=(X^2+Y^2)Y^2
\n" ); document.write( "CB = Y*SQRT(X^2+Y^2)
\n" ); document.write( " \n" ); document.write( "
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