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.
a2+b2=c2
(10 points)
Path Length=
yards
Using the Pythagorean theorem, we can find the length of the diagonal path. Let's label the length as "c" and the sides of the rectangle as "a" and "b".
a = 40 yards
b = 80 yards
c = ?
According to the Pythagorean theorem,
a^2 + b^2 = c^2
Substituting the values,
40^2 + 80^2 = c^2
Simplifying,
1600 + 6400 = c^2
8000 = c^2
Taking the square root of both sides,
√8000 = c
c ≈ 89.44 yards
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, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the length of one side of the park is 40 yards (width), and the length of the other side is 80 yards (length). Let's use these values.
Let's call the diagonal path the hypotenuse, which we'll label as 'c'.
According to the Pythagorean theorem, we have:
a^2 + b^2 = c^2,
where a and b are the two sides of the rectangle, and c is the length of the diagonal path.
Plugging in the values, we get:
40^2 + 80^2 = c^2,
1600 + 6400 = c^2,
8000 = c^2.
To find c, we need to take the square root of both sides:
c = √(8000) ≈ 89.4.
Therefore, the length of the diagonal path in the rectangular park is approximately 89.4 yards, rounded to the nearest tenth.
To find the length of the diagonal path of 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 side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the rectangle are 40 yards and 80 yards. Let's label one side as 'a' and the other side as 'b', and the diagonal as 'c'. We can use the Pythagorean theorem equation:
a^2 + b^2 = c^2
Substituting the values:
40^2 + 80^2 = c^2
Simplifying:
1600 + 6400 = c^2
8000 = c^2
To find 'c', we need to take the square root of both sides of the equation:
√8000 = c
Calculating the square root:
c ≈ 89.44 yards
Rounding to the nearest tenth, the length of the diagonal path will be approximately 89.4 yards.