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, 44AD=44 and D, C, equals, 4, commaDC=4, what is the length of start overline, B, D, end overline
BD
in simplest radical form?

Answer 1

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

BD = sqrt(44·4) = sqrt(176) = 4√11.