1. **State the problem:** We have a right triangle with vertices Aurora, Burlington, and Clifton. The side Aurora-Burlington is 65 km, Burlington-Clifton is $x$ km, and the hypotenuse Aurora-Clifton is 97 km. 2. **Identify the right angle:** Since Aurora-Clifton is the hypotenuse, the right angle is at Burlington. 3. **Use the Pythagorean theorem:** For a right triangle with legs $a$ and $b$ and hypotenuse $c$, we have $$a^2 + b^2 = c^2.$$ Here, $a = 65$, $b = x$, and $c = 97$. 4. **Calculate $x$:** $$65^2 + x^2 = 97^2$$ $$4225 + x^2 = 9409$$ $$x^2 = 9409 - 4225 = 5184$$ $$x = \sqrt{5184} = 72$$ 5. **Calculate the distances:** - Direct distance from Aurora to Clifton is 97 km. - Distance from Aurora to Clifton through Burlington is $65 + 72 = 137$ km. 6. **Find how much closer the direct route is:** $$137 - 97 = 40$$ **Answer:** It is 40 km closer to travel directly from Aurora to Clifton than through Burlington.