document.write( "Question 837675: ABC is a right angle triangle ,where angle b= 90 degree . BD drawn perpendicular to AC . AD=9 DC= 16. Find AB \n" ); document.write( "

Algebra.Com's Answer #504741 by KMST(5328) $\"\"$ $\"About$

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\n" ); document.write( "The altitude BD splits right triangle ABC into right triangles ADB and BCD.
\n" ); document.write( "They are all similar right triangles.
\n" ); document.write( "The ratio {leg adjacent to angle BAC)/hypotenuse is
\n" ); document.write( " $\"AB%2FAC=AB%2F%28AD%2BDC%29\"$ in triangle ABC,
\n" ); document.write( "and it is $\"AD%2FAB\"$ in triangle ADB.
\n" ); document.write( "Since those two triangles are similar, those ratios are the same,
\n" ); document.write( "so $\"AB%2F%28AD%2BDC%29=AD%2FAB\"$ <--> $\"%28AB%29%5E2=AD%2A%28AD%2BDC%29\"$ .
\n" ); document.write( "Substituting numbers,
\n" ); document.write( " $\"%28AB%29%5E2=9%289%2B16%29\"$
\n" ); document.write( " $\"%28AB%29%5E2=9%2A25\"$
\n" ); document.write( " $\"%28AB%29%5E2=3%5E2%2A5%5E2\"$
\n" ); document.write( " $\"%28AB%29%5E2=%283%2A5%29%5E2\"$
\n" ); document.write( " $\"%28AB%29%5E2=15%5E2\"$
\n" ); document.write( " $\"highlight%28AB=15%29\"$ \n" ); document.write( "

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