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, 12AD=12 and B, D, equals, 24, commaBD=24, what is the length of start overline, A, C, end overline, question mark
AC
?

Answer 1

In a right triangle with altitude from the right angle to the hypotenuse, the segments satisfy BD^2 = AD·DC. So

DC = BD^2 / AD = 24^2 / 12 = 576/12 = 48.

Thus AC = AD + DC = 12 + 48 = 60.