A right triangle has a hypotenuse of length $8$ and one leg of length $5$. What is the length of the other leg?

Let the unknown leg have length $x$. By the Pythagorean theorem, **hypotenuse squared equals the sum of the squares of the two legs**: $8^{2} = 5^{2} + x^{2} \Rightarrow 64 = 25 + x^{2} \Rightarrow x^{2} = 39 \Rightarrow x = \sqrt{39} \approx 6.2$. Why the others fail: - **A** ($3$) comes from $8 - 5 = 3$ — Pythagorean lengths are not subtracted, they're squared. - **C** ($\sqrt{89}$) is what you'd get if you treated the hypotenuse as a leg: $5^{2} + 8^{2} = 89$. The hypotenuse is always the **longest** side. - **D** ($13$) is $5 + 8$ — that's the perimeter trap, not Pythagoras.