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, 65, commaDC=65, what is the length of start overline, B, D, end overline
BD
in simplest radical form?

Answer 1

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

BD = sqrt(6·65) = sqrt(390).

Thus BD = √390 (simplest radical form).