A rectangular park that measures 31 yards by 67 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 is?
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 (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length 31 yards as the base (b) and the length 67 yards as the height (h).
Using the Pythagorean theorem, we have:
diagonal^2 = base^2 + height^2
diagonal^2 = 31^2 + 67^2
diagonal^2 = 961 + 4489
diagonal^2 = 5450
diagonal ≈ √5450
diagonal ≈ 73.8 yards
Therefore, the length of the diagonal path will be approximately 73.8 yards when rounded to the nearest tenth.
To find the length of the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides.
In this case, the length (a) is 31 yards and the width (b) is 67 yards.
Using the Pythagorean theorem, we have:
diagonal^2 = length^2 + width^2
Substituting the values, we get:
diagonal^2 = 31^2 + 67^2
Calculating:
diagonal^2 = 961 + 4489
diagonal^2 = 5450
Taking the square root of both sides:
diagonal = sqrt(5450)
Rounding to the nearest tenth:
diagonal ≈ 73.8 yards
Therefore, the length of the diagonal path will be approximately 73.8 yards.
To find the length of the diagonal of a rectangle, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right 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 lengths of the other two sides.
In this case, the two sides of the rectangle are 31 yards and 67 yards, and the diagonal is the hypotenuse.
So, if we let "d" represent the length of the diagonal, we can set up the equation:
d^2 = 31^2 + 67^2
To solve for "d", we can calculate the squares of 31 and 67, add them together, and then take the square root of the sum.
Using a calculator or a computer program, we can find that:
31^2 = 961
67^2 = 4489
So,
d^2 = 961 + 4489
d^2 = 5450
To find the value of "d", we can take the square root of both sides:
d ≈ √5450
Using a calculator or a computer program, we find that the square root of 5450 is approximately 73.8.
Therefore, the length of the diagonal path in the rectangular park will be approximately 73.8 yards when rounded to the nearest tenth.