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, 6AD=6 and D, C, equals, 11, commaDC=11, what is the length of start overline, B, D, end overline
BD
in simplest radical form?

Answer 1

In a right triangle, the altitude to the hypotenuse satisfies BD^2 = AD·DC. So BD = sqrt(6·11) = sqrt(66).