a rectangular park that measures 31 yards by 67 yards will have a diagonal path built. How long will the path be? round the answer to the nearest tenth
To find the length of the diagonal path, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal path) is equal to the sum of the squares of the other two sides.
The length of one side of the rectangle is 31 yards, and the length of the other side is 67 yards. So, by applying the Pythagorean theorem, we can find the square of the diagonal path:
Diagonal² = 31² + 67²
Diagonal² = 961 + 4489
Diagonal² = 5450
To find the length of the diagonal path, we need to take the square root of both sides:
Diagonal = √5450
Using a calculator, we find that the diagonal is approximately 73.9 yards. Rounding to the nearest tenth, the length of the diagonal path is 73.9 yards.