What is the length of the diagonal for the given rectangular prism to the nearest whole unit?
Length- 8cm
Width- 3cm
Height- 7cm
Using the Pythagorean theorem, we can calculate the length of the diagonal of the rectangular prism.
The diagonal can be thought of as the hypotenuse of a right-angled triangle, where the length, width, and height of the rectangular prism are the other sides of the triangle.
The formula for the length (L) of the diagonal is:
L = √(l² + w² + h²)
where l is the length, w is the width, and h is the height.
Substituting the values given:
L = √(8² + 3² + 7²)
L = √(64 + 9 + 49)
L = √122
L ≈ 11
Therefore, the length of the diagonal of the rectangular prism is about 11 cm (rounded to the nearest whole unit).
To find the length of the diagonal of a rectangular prism, 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 side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length, width, and height of the rectangular prism form the three sides of a right-angled triangle, with the diagonal being the hypotenuse.
Using the given dimensions:
Length = 8 cm
Width = 3 cm
Height = 7 cm
We can calculate the diagonal as follows:
Step 1: Calculate the square of the length, width, and height.
Length^2 = 8^2 = 64
Width^2 = 3^2 = 9
Height^2 = 7^2 = 49
Step 2: Add the squares of the length, width, and height.
64 + 9 + 49 = 122
Step 3: Take the square root of the sum to find the length of the diagonal.
√122 ≈ 11.045
To the nearest whole unit, the length of the diagonal is approximately 11 cm.
To find the length of the diagonal of a rectangular prism, we can use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the length, width, and height of the prism.
Using the Pythagorean theorem, we have:
diagonal^2 = length^2 + width^2 + height^2
Plugging in the given values, we get:
diagonal^2 = 8^2 + 3^2 + 7^2
diagonal^2 = 64 + 9 + 49
diagonal^2 = 122
To find the length of the diagonal, we take the square root of both sides:
diagonal = sqrt(122)
Evaluating this, we get:
diagonal ≈ 11 cm
Therefore, the length of the diagonal of the given rectangular prism, to the nearest whole unit, is 11 cm.