A rectangular park that measures 40 yards by 80 yards will have a diagonal path built. How long will the path be? Round your answer to the nearest tenth. Click Here for Help Video.(1 point)
yards
To find the length of the diagonal path, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal path forms the hypotenuse of a right triangle with sides measuring 40 yards and 80 yards.
Using the Pythagorean theorem, we can calculate the length of the diagonal path:
diagonal path = √(40^2 + 80^2)
= √(1600 + 6400)
= √8000
≈ 89.44 yards
So the length of the diagonal path will be approximately 89.44 yards.
To find the length of the diagonal path, you can use the Pythagorean theorem. According to the theorem, the square of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides.
In this case, the two other sides are the length and width of the rectangular park: 40 yards and 80 yards, respectively.
So, the equation can be written as:
diagonal^2 = 40^2 + 80^2
Calculating this, we get:
diagonal^2 = 1600 + 6400 = 8000
Now, to find the length of the diagonal, we take the square root of both sides:
diagonal = sqrt(8000)
Using a calculator, the square root of 8000 is approximately 89.4.
Therefore, the length of the diagonal path will be approximately 89.4 yards (rounded to the nearest tenth).
To find the length of the diagonal path in the rectangular park, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the length and width of the park are the two sides of the right triangle, and the diagonal path is the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the diagonal path as follows:
diagonal path length^2 = length^2 + width^2
diagonal path length^2 = 40^2 + 80^2
diagonal path length^2 = 1600 + 6400
diagonal path length^2 = 8000
To find the length of the diagonal path, we need to take the square root of both sides:
diagonal path length ≈ √8000
Using a calculator, we find that diagonal path length ≈ 89.4.
Therefore, the length of the diagonal path in the rectangular park is approximately 89.4 yards, rounded to the nearest tenth.