A rectangular park that measures 45 yards by 31 yards will have a diagonal path built. How long will the path be? Round your answer to the nearest tenth.
We can use the Pythagorean Theorem to find the length of the diagonal path.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse (the longest side of the triangle).
In this case, the two legs of the right triangle formed by the rectangular park are 45 yards and 31 yards, and we want to find the length of the diagonal path (the hypotenuse).
Using the Pythagorean Theorem, we have:
length of diagonal path = √(45^2 + 31^2)
length of diagonal path = √(2025 + 961)
length of diagonal path = √2986
length of diagonal path ≈ 54.67 yards
Rounded to the nearest tenth, the length of the diagonal path is approximately 54.7 yards.