To apply the Pythagorean Theorem to find the length of the diagonal of a square, we can use the formula:
diagonal^2 = side^2 + side^2
Since a square has all sides equal, we can replace "side" with "s" in the formula:
diagonal^2 = s^2 + s^2
Simplifying this equation gives us:
diagonal^2 = 2s^2
To find the length of the diagonal, we can take the square root of both sides:
diagonal = √(2s^2)
Since we are asked to round our answer to the nearest hundredth, let's consider an example where the side length of the square is 5 units.
diagonal = √(2 * 5^2)
diagonal = √(2 * 25)
diagonal = √50
diagonal ≈ 7.07
Therefore, the length of the diagonal of the square is approximately 7.07 units.
Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary
5 answers
Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3). Round your answer to the nearest hundredth, if necessary
To apply the Pythagorean Theorem to find the length between two points in a coordinate plane, we need to find the horizontal and vertical distances between the points.
Given the coordinates (2, 5) and (7, 3), the horizontal distance is the difference between the x-coordinates and the vertical distance is the difference between the y-coordinates:
Horizontal distance = 7 - 2 = 5
Vertical distance = 3 - 5 = -2
However, since we are using the Pythagorean Theorem, we need the distance to be positive. Therefore, we can take the absolute value of the vertical distance:
|Vertical distance| = |-2| = 2
Now, we have a right triangle with a horizontal leg of length 5 and a vertical leg of length 2. We can apply the Pythagorean Theorem:
(diagonal)^2 = (horizontal distance)^2 + (vertical distance)^2
(diagonal)^2 = 5^2 + 2^2
(diagonal)^2 = 25 + 4
(diagonal)^2 = 29
To find the length of the diagonal itself, we take the square root:
diagonal = √29
Rounding to the nearest hundredth, we find:
diagonal ≈ 5.39
Therefore, the length between the points (2, 5) and (7, 3) is approximately 5.39.
Given the coordinates (2, 5) and (7, 3), the horizontal distance is the difference between the x-coordinates and the vertical distance is the difference between the y-coordinates:
Horizontal distance = 7 - 2 = 5
Vertical distance = 3 - 5 = -2
However, since we are using the Pythagorean Theorem, we need the distance to be positive. Therefore, we can take the absolute value of the vertical distance:
|Vertical distance| = |-2| = 2
Now, we have a right triangle with a horizontal leg of length 5 and a vertical leg of length 2. We can apply the Pythagorean Theorem:
(diagonal)^2 = (horizontal distance)^2 + (vertical distance)^2
(diagonal)^2 = 5^2 + 2^2
(diagonal)^2 = 25 + 4
(diagonal)^2 = 29
To find the length of the diagonal itself, we take the square root:
diagonal = √29
Rounding to the nearest hundredth, we find:
diagonal ≈ 5.39
Therefore, the length between the points (2, 5) and (7, 3) is approximately 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.
To apply the Pythagorean Theorem to find the length between two points in a coordinate plane, we need to find the horizontal and vertical distances between the points.
Given the coordinates (-1, 6) and (5, -2), the horizontal distance is the difference between the x-coordinates and the vertical distance is the difference between the y-coordinates:
Horizontal distance = 5 - (-1) = 6
Vertical distance = -2 - 6 = -8
However, since we are using the Pythagorean Theorem, we need the distance to be positive. Therefore, we can take the absolute value of the vertical distance:
|Vertical distance| = |-8| = 8
Now, we have a right triangle with a horizontal leg of length 6 and a vertical leg of length 8. We can apply the Pythagorean Theorem:
(diagonal)^2 = (horizontal distance)^2 + (vertical distance)^2
(diagonal)^2 = 6^2 + 8^2
(diagonal)^2 = 36 + 64
(diagonal)^2 = 100
To find the length of the diagonal itself, we take the square root:
diagonal = √100
Rounding to the nearest hundredth, we find:
diagonal = 10
Therefore, the length between the points (-1, 6) and (5, -2) is 10 units.
Given the coordinates (-1, 6) and (5, -2), the horizontal distance is the difference between the x-coordinates and the vertical distance is the difference between the y-coordinates:
Horizontal distance = 5 - (-1) = 6
Vertical distance = -2 - 6 = -8
However, since we are using the Pythagorean Theorem, we need the distance to be positive. Therefore, we can take the absolute value of the vertical distance:
|Vertical distance| = |-8| = 8
Now, we have a right triangle with a horizontal leg of length 6 and a vertical leg of length 8. We can apply the Pythagorean Theorem:
(diagonal)^2 = (horizontal distance)^2 + (vertical distance)^2
(diagonal)^2 = 6^2 + 8^2
(diagonal)^2 = 36 + 64
(diagonal)^2 = 100
To find the length of the diagonal itself, we take the square root:
diagonal = √100
Rounding to the nearest hundredth, we find:
diagonal = 10
Therefore, the length between the points (-1, 6) and (5, -2) is 10 units.
7 answers