Find the Hypotenuse m in Right Triangle ABC with Legs 1 and 2

To find the length of the hypotenuse $m$ in right triangle $\triangle ABC$, we will use the Pythagorean Theorem: $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs and $c$ is the hypotenuse.

• Step 1: Identify the lengths of the legs. Here, $a = 2$ and $b = 1$.
• Step 2: Apply the Pythagorean Theorem: $(2)^2 + (1)^2 = m^2$.
• Step 3: Calculate: $4 + 1 = 5$.
• Step 4: Solve for $m$ by taking the square root: $m = \sqrt{5}$.

Therefore, the length of the hypotenuse $m$ is $\sqrt{5}$.

This matches the provided answer choice: $\sqrt{5}$ (choice 4).