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, B, equals, 10AB=10 and A, D, equals, 5, commaAD=5, 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 projection theorem gives AB^2 = AD·AC. So

AC = AB^2 / AD = 10^2 / 5 = 100 / 5 = 20.

Thus AC = 20.