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, 33AD=33 and D, C, equals, 13, commaDC=13, 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. Thus

BD = sqrt(AD · DC) = sqrt(33 · 13) = sqrt(429).

So BD = sqrt(429).