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#40303

area

geometry

hard

90 sec

Refer to the figure: In right triangle $A BC$ with right angle at $C$ , the base $A C$ is divided into segments of lengths 3 and 9 by a perpendicular from a point on $A B$ to $A C$ . This perpendicular has length $x$ , and the vertical leg $BC$ has length $y$ . If the area of triangle $A BC$ is 54, what is the value of $x$ ?

• Up to 5 characters (6 if negative). Only numbers, decimal (.), fraction (/), negative (-).
• Fractions must be in lowest terms.
• Mixed numbers must be converted to improper fractions.