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, 11AD=11 and D, C, equals, 7, commaDC=7, 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(11·7) = sqrt(77).

Thus BD = √77.