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#12605

similarity

geometry

right triangles

hard

120 sec

In right triangle $X Y Z$ , $∠ Z$ is the right angle and $Y Z = 75$ . Point $U$ on side $X Y$ is connected by a line segment with point $V$ on side $XZ$ such that line segment $U V$ is parallel to side $Y Z$ and $X V = \frac{1}{2} XZ$ . What is the length of line segment $U V$ ?

• 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.