Question

If BD = 4, AD = x-6, and CD = x, what is the length of CD?

Answer 1

Answer:

The length of CD is 8 units

Step-by-step explanation:

The complete question in the attached figure

we know that

According to the Right Triangle Altitude Theorem,

$(BD)^2 = (AD)(CD)$

substitute the given values

$(4)^2 = (x-6)(x)$

$16=x^2-6x\\x^2-6x-16=0$

solve the quadratic equation by graphing

The solution is x=8 or x=-6

see the attached figure N 2

Discard the negative length.

therefore

The length of CD is 8 units