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, 8AD=8 and B, D, equals, 16, commaBD=16, 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 altitude satisfies BD^2 = AD·DC. Given AD = 8 and BD = 16:

16^2 = 8·DC → 256 = 8·DC → DC = 32.

Then AC = AD + DC = 8 + 32 = 40.