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, 2AD=2 and D, C, equals, 2, commaDC=2, what is the length of start overline, B, D, end overline, question mark
BD
?

Answer 1

In a right triangle with altitude from the right angle to the hypotenuse, the altitude length satisfies BD^2 = AD·DC. Here AD = DC = 2, so

BD = sqrt(AD·DC) = sqrt(2·2) = sqrt(4) = 2.