Question

Because of the increase in traffic between Springfield and Orangeville, a new road was built to connect the two towns. The old road goes south x miles from Springfield to Freeport and then goes east x + 5 miles from Freeport to Orangeville. The new road is 9 miles long and goes straight from Springfield to Orangeville. Find the number of miles that a person drove using the old road. Please help ASAP!!! :(

Answer 1

Answer:

11.70 miles

Explanation:

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