Question

Given right triangle A, B, CABC with altitude start overline, B, D, end overline
BD
drawn to hypotenuse start overline, A, C, end overline
AC
. If A, D, equals, 16AD=16 and D, C, equals, 44, commaDC=44, what is the length of start overline, B, D, end overline
BD
in simplest radical form?

Answer 1

In a right triangle with altitude to the hypotenuse, BD^2 = AD·DC. So

BD = sqrt(16·44) = sqrt(704) = sqrt(64·11) = 8√11.