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, C, equals, 2BC=2 and D, C, equals, 1, commaDC=1, what is the length of start overline, A, C, end overline, question mark
AC
?

Answer 1

AC = 4.

Reason: In a right triangle with altitude from the right angle to the hypotenuse, each leg is the geometric mean of the hypotenuse and the adjacent hypotenuse segment. So BC^2 = AC·DC. With BC = 2 and DC = 1, 2^2 = AC·1, hence AC = 4.