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, 5AD=5 and B, D, equals, 15, commaBD=15, what is the length of start overline, A, C, end overline, question mark
AC
?

Answer 1

Use the altitude-to-hypotenuse relation BD^2 = AD·DC.

Given AD = 5 and BD = 15, we have 15^2 = 5·DC ⇒ DC = 225/5 = 45. Thus AC = AD + DC = 5 + 45 = 50.