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, 15AD=15 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 with altitude from the right angle to the hypotenuse, BD^2 = AD·DC. So

BD = sqrt(15·22) = sqrt(330).

Since 330 = 2·3·5·11 has no repeated factors, the simplest radical form is sqrt(330).