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 B, D, equals, 4BD=4 and D, C, equals, 2, commaDC=2, what is the length of start overline, A, D, end overline, question mark
AD
?

Answer 1

In a right triangle with altitude from the right angle to the hypotenuse, the altitude length h satisfies h^2 = (segment1)(segment2) of the hypotenuse. Here BD is the altitude, so

BD^2 = AD · DC.

Given BD = 4 and DC = 2:

AD = BD^2 / DC = 4^2 / 2 = 16 / 2 = 8.

So AD = 8.