Calculate the length of the diagonal for the given rectangular prism. Length: 10 cm Width: 4 cm Height: 10 cm
Pls help
Literally anyone?
It’s been 9 years bro
To calculate the length of the diagonal of a rectangular prism, 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, we need to find the length of the diagonal, which is the hypotenuse of a right triangle formed by the three dimensions of the rectangular prism. Let's label the length, width, and height as follows:
Length: L = 10 cm
Width: W = 4 cm
Height: H = 10 cm
Now, we can use the Pythagorean theorem to find the length of the diagonal. We have two sides of the triangle: L and W. Let's call the diagonal D.
According to the Pythagorean theorem:
D^2 = L^2 + W^2
Substituting the given values:
D^2 = (10 cm)^2 + (4 cm)^2
Simplifying:
D^2 = 100 cm^2 + 16 cm^2
D^2 = 116 cm^2
Taking the square root of both sides:
D = √116 cm
Calculating the square root:
D ≈ 10.77 cm
Therefore, the length of the diagonal of the rectangular prism is approximately 10.77 cm.