In right triangle $xyz$, if $xy$ is $4$ units and $yz$ is $4$ units, what is the length of line segment $xz$?

• A. $20$ units
• B. $\sqrt{32}$ units
• C. $8$ units
• D. $4$ units

Answer: (B)

Verified step by step guidance

1. Identify the right triangle and label the sides: given triangle \( xyz \) is right-angled, with sides \( xy = 4 \) units and \( yz = 4 \) units.
2. Recognize that the side \( xz \) is the hypotenuse of the right triangle since it is opposite the right angle.
3. Apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: \[ xz^2 = xy^2 + yz^2 \]
4. Substitute the known side lengths into the equation: \[ xz^2 = 4^2 + 4^2 \]
5. Simplify the right side and then take the square root to find \( xz \): \[ xz = \sqrt{4^2 + 4^2} = \sqrt{16 + 16} = \sqrt{32} \]