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, 3AD=3 and D, C, equals, 3, commaDC=3, what is the length of start overline, B, D, end overline, question mark
BD
?

Answer 1

Drop from the right angle B to the hypotenuse AC at D. By similarity of triangles, BD^2 = AD·DC. So BD = sqrt(3·3) = sqrt(9) = 3.