<h3>Answer:</h3>
11.70 miles
<h3>Explanation:</h3>
The road from Springfield to Orangeville is apparently the hypotenuse of a right triangle whose legs are x and x+5. The value of x can be found from the Pythagorean theorem:
... 9² = x² + (x+5)²
... 2x² +10x -56 = 0 . . . . . . eliminate parentheses, collect terms, subtract 81.
... x² +5x -28 = 0 . . . . . . . . divide by 2 (because we can)
... x² +5x +6.25 = 28 +6.25 . . . . add 28, then add (5/2)² to complete the square
... (x +5/2) = √34.25 . . . . . . . .take the positive square root
... x = -2.5 +√34.25 ≈ 3.352
The total distance via the old road is the sum of the leg lengths:
... x + (x+5) = 2x +5 = 2(3.352) +5 = 11.704 . . . . miles
