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.
The length of the diagonal can be found using the Pythagorean theorem: c^2 = a^2 + b^2, where c is the length of the diagonal, and a and b are the lengths of the sides of the rectangle.
In this case, a = 40 yards and b = 80 yards. Thus, c^2 = 40^2 + 80^2.
Using a calculator, 40^2 + 80^2 = 6400 + 6400 = 12800.
Therefore, c^2 = 12800, and taking the square root of both sides, c = sqrt(12800) = 112.92 yards.
Rounding to the nearest tenth, the length of the path will be approximately 112.9 yards.
To find the length of the diagonal path, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, the length of one side of the rectangle is 40 yards and the length of the other side is 80 yards. The diagonal path will be the hypotenuse of a right triangle formed by these two sides.
Applying the Pythagorean theorem, we have:
c^2 = a^2 + b^2
Substituting the given values, we have:
c^2 = 40^2 + 80^2
Calculating this equation, we get:
c^2 = 1600 + 6400
c^2 = 8000
To find the length of the diagonal path (c), we take the square root of both sides of the equation:
c = sqrt(8000)
Using a calculator, the approximate value of the square root of 8000 is 89.4.
Therefore, the length of the diagonal path will be approximately 89.4 yards.
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-angled 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 park can be seen as a right-angled triangle, where the length of one side is 40 yards and the length of the other side is 80 yards. Let's call the length of the diagonal path "d."
Using the Pythagorean theorem, we have:
d^2 = 40^2 + 80^2
Simplifying,
d^2 = 1600 + 6400
d^2 = 8000
To find the value of "d," we take the square root of both sides:
d = √8000
Using a calculator, we find:
d ≈ 89.4
Rounding to the nearest tenth, the length of the diagonal path is approximately 89.4 yards.