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, 4AD=4 and D, C, equals, 4, commaDC=4, what is the length of start overline, B, D, end overline, question mark
BD
?
x
4
A
B
D
C
4
Answer
Attempt 1 out of 2

x, equalsx=

Answer 1

BD is the altitude to the hypotenuse, so it satisfies the geometric-mean relation BD^2 = AD·DC. Thus BD = sqrt(4·4) = sqrt(16) = 4.