Calculate the length of the diagonal for the given rectangular prism. It says length hight width
but in the lesson it says length hight deph how to i find the diagonal example
how to get diagonal saying lenght hight width
another simple name for "rectangular prism" is a box
let the
length be x
width be y
height be z
By the diagonal of the box they want the line from a bottom corner to the opposite corner at the top
(think of placing a stick inside the box, where would the longest stick go ?? )
let the diagonal of the base be d
d^2 = x^2 + y^2
now look at the right - angled triangle formed by that diagonal, the height and our stick
let the length of the long diagonal (our stick) be k
then k^2 = d^2 + z^2 , but d^2 = x^2 + y^2
so k^2 = x^2 + y^2 + z^2
e.g. suppose you have a box which is
12 cm by 10 cm by 8 cm
the diagonal = √(12^2+10^2+8^2) = √308 or appr 17.55 cm
To calculate the length of the diagonal of a rectangular prism, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In a rectangular prism, the diagonal is the hypotenuse of a right triangle formed by the three edges that meet at a common vertex (corner). The lengths of these three edges are the length, height, and depth, which represent the three dimensions of the prism.
To find the diagonal, you need to know the values of the length, height, and depth. Let's say the length is represented by "L," the height by "H," and the depth by "D."
Using the Pythagorean theorem, the formula to calculate the length of the diagonal (D) is:
D = √(L^2 + H^2 + D^2)
Simply substitute the values of L, H, and D into the formula and calculate the square root of the sum to find the length of the diagonal.
However, in your question, you mentioned that the dimensions given are length, height, and width, while the lesson states length, height, and depth. If the dimensions given are length, height, and width, you can still use the same formula. The width can be considered as the depth or the third dimension of the rectangular prism.
To summarize:
1. Identify the values of the length (L), height (H), and depth (D) or width of the rectangular prism.
2. Use the formula D = √(L^2 + H^2 + D^2) to calculate the length of the diagonal.
3. Substitute the values of L, H, and D (or width) into the formula and calculate the square root of the sum to find the length of the diagonal.