GIVEN: BC = 24. Add this to the diagram.
Also, let x = the length of CD


GIVEN: AB = (1/2)(CD)
Since CD has length x, we know that 0.5x = the length of AB


GIVEN: BD = (3/2)(AC)
BD has length 24 + x
AC has length 24 + 0.5x
So, we can write: 24 + x = (3/2)(24 + 0.5x)
Expand right side to get: 24 + x = 36 + 0.75x
Subtract 0.75x from both sides to get: 24 + 0.25x = 36
Subtract 24 from both sides to get: 0.25x = 12
Solve: x = 48
If x = 48, then 0.5x = 24

Add this information to the diagram:


Length of AD = 24 + 24 + 48
= 96

Answer: D

Cheers,
Brent

A B C D

unknown, 24, unknown


\(\frac{3}{2}\)*(\(\frac{x}{2}\) + 24) = 24 + x

x = 48

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