Question

what is xy?a. $sqrt{2}$b. 5c. $5sqrt{2}$d. 10

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so legs are equal. $XZ = YZ = 5$

Step2: Apply Pythagorean theorem

Use $XY^2 = XZ^2 + YZ^2$
$$XY^2 = 5^2 + 5^2 = 25 + 25 = 50$$

Step3: Solve for XY

Take square root of both sides.
$$XY = \sqrt{50} = 5\sqrt{2}$$

Answer:

C. $5\sqrt{2}$