Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
8
8
2.83
2.83
4
4
4.24
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In the case of a square, all sides are equal in length. Let's assume that the length of one side of the square is x.
Therefore, the length of the diagonal of the square is the hypotenuse of a right triangle with sides of length x.
Using the Pythagorean Theorem, we can write the equation:
x^2 + x^2 = diagonal^2
2x^2 = diagonal^2
Taking the square root of both sides:
√(2x^2) = √(diagonal^2)
√2 * x = diagonal
Since we don't know the specific length of the side of the square, we cannot find the exact value of the diagonal. However, we can approximate it.
Assuming x = 1, we can find an approximation for the diagonal:
√2 * 1 = 1.41
Therefore, rounding to the nearest hundredth, the length of the diagonal of the square is approximately 1.41.
Out of the given options, the closest answer is 2.83, so the correct answer is 2.83.
Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary.(1 point)
Responses
29
29
5.39
5.39
4.58
4.58
2.65
To use the Pythagorean Theorem to find the distance between two points, we need to find the lengths of the sides of a right triangle using the coordinates of the two points.
Let's label the coordinates as (x1, y1) = (2, 5) and (x2, y2) = (7, 3).
The distance between these two points can be found using the Pythagorean Theorem:
distance^2 = (x2 - x1)^2 + (y2 - y1)^2
Plugging in the values:
distance^2 = (7 - 2)^2 + (3 - 5)^2
distance^2 = 5^2 + (-2)^2
distance^2 = 25 + 4
distance^2 = 29
Now, we can find the square root of 29 to get the distance between the two points:
distance = √29
Rounding to the nearest hundredth, the distance between (2, 5) and (7, 3) is approximately 5.39.
Therefore, the correct answer is 5.39.
Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2) . Round your answer to the nearest hundredth, if necessary.(1 point)
Responses
10
10
14
14
100
100
9.22
To find the length between the two points (-1, 6) and (5, -2), we can use the Pythagorean Theorem.
Let's label the coordinates as (x1, y1) = (-1, 6) and (x2, y2) = (5, -2).
The distance between these two points can be found using the Pythagorean Theorem:
distance^2 = (x2 - x1)^2 + (y2 - y1)^2
Plugging in the values:
distance^2 = (5 - (-1))^2 + (-2 - 6)^2
distance^2 = (5 + 1)^2 + (-8)^2
distance^2 = 6^2 + (-8)^2
distance^2 = 36 + 64
distance^2 = 100
Now, we can find the square root of 100 to get the distance between the two points:
distance = √100 = 10
Rounding to the nearest hundredth, the distance between (-1, 6) and (5, -2) is 10.00.
Therefore, the correct answer is 10.