Geometry question, length of the line in a right triangle

In right triangle ABC, the legs line AC and line BC measures 6 and 8 respectively.

Altitude line CD is drawn to the hypotenuse of triangle ABC.

What is the length of line AD?

AD=x, DB=10-x, AB=10

36-x^2=64-(10-x^2)

x=?
x=3.6 or

36=x(10)
x=3.6

or
64=(10-x)(10)
x=3.6

Hello

Let's
AC = b
CB = a
AB = c
CD = d
AD = m
DB = p

c² = a² + b² = 36 + 64 = 100
c = 10

m + p = 10

In triangle ADC
d² = b² - m²

In triangle CDB
d² = a² - p²

So a² - p² = b² - m²
a² - b² = p² - m²
64 - 36 = p² - m²
p² - m² = 28

and

p + m = 10
m = 10 - p

p² - (10 - p)² = 28
p² - (100 - 20p + p²) = 28
p² - 100 + 20p - p² = 28
20p = 128
p = 6.4

m = 3.6 = AD ===>Answer

Hope it helps

It isfair to select a best answer, whatever it is. Thank you !

Bye !