A rectangular park that measures 40 yards by 80 yards will have a diagonal path built. How long will the diagonal path be? Round your answer to the nearest tenth.
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 length of the hypotenuse (in this case, the diagonal path) is equal to the sum of the squares of the other two sides (the sides of the rectangle).
Let's call the length of the rectangle 40 yards and the width 80 yards. Then, using the Pythagorean theorem, we have:
diagonal path^2 = 40^2 + 80^2
diagonal path^2 = 1600 + 6400
diagonal path^2 = 8000
Now, we can take the square root of both sides to find the length of the diagonal path:
diagonal path = √8000
diagonal path ≈ 89.4 yards
Rounded to the nearest tenth, the diagonal path will be approximately 89.4 yards.
To find the length of the diagonal path, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the sides of the rectangle represent the two legs of the right-angled triangle, and the diagonal path represents the hypotenuse. We can label one side as the length (L) of the rectangle (80 yards) and the other side as the width (W) of the rectangle (40 yards).
Applying the Pythagorean theorem, we have:
Diagonal path^2 = Length^2 + Width^2
Diagonal path = √(Length^2 + Width^2)
Substituting the given values, we get:
Diagonal path = √(80^2 + 40^2)
Calculating the above equation:
Diagonal path = √(6400 + 1600)
= √(8000)
≈ 89.44
Therefore, the length of the diagonal path, rounded to the nearest tenth, is approximately 89.4 yards.
To find the length of the diagonal path in the rectangular park, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length of the rectangular park represents one side, and the width represents the other side. The diagonal path will then act as the hypotenuse.
Let's calculate the length of the diagonal path.
Using the Pythagorean theorem:
diagonal path^2 = length^2 + width^2
Substituting the given values:
diagonal path^2 = 40^2 + 80^2
Calculating the squares:
diagonal path^2 = 1600 + 6400
diagonal path^2 = 8000
Taking the square root of both sides:
diagonal path = √8000
Using a calculator:
diagonal path ≈ 89.44 yards (rounded to the nearest tenth)
Therefore, the length of the diagonal path in the rectangular park is approximately 89.44 yards.