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, 4AD=4 and D, C, equals, 22, commaDC=22, 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(4 · 22) = sqrt(88) = 2√22.