1. **State the problem:** We want to find how much closer it is to travel directly from Aurora to Clifton than going from Aurora to Clifton through Burlington. 2. **Identify the triangle and given sides:** The triangle has vertices Aurora, Burlington, and Clifton with a right angle at Burlington. - Aurora to Clifton (hypotenuse) = 97 - Aurora to Burlington = 65 - Burlington to Clifton = $x$ (unknown) 3. **Use the Pythagorean theorem:** For a right triangle with legs $a$ and $b$, and hypotenuse $c$, the relation is: $$a^2 + b^2 = c^2$$ Here, legs are Aurora to Burlington and Burlington to Clifton, hypotenuse is Aurora to Clifton. 4. **Set up the equation:** $$65^2 + x^2 = 97^2$$ 5. **Calculate squares:** $$4225 + x^2 = 9409$$ 6. **Isolate $x^2$:** $$x^2 = 9409 - 4225$$ $$x^2 = 5184$$ 7. **Find $x$ by taking the square root:** $$x = \sqrt{5184} = 72$$ 8. **Calculate the difference in travel distances:** - Direct distance Aurora to Clifton = 97 - Distance via Burlington = Aurora to Burlington + Burlington to Clifton = $65 + 72 = 137$ 9. **Difference:** $$137 - 97 = 40$$ **Answer:** It is 40 units closer to travel directly from Aurora to Clifton than going through Burlington.