Calculate the length of the diagonal for the given rectangular prism. Round to the nearest tenth
length 10 cm
width 4 cm
height 10
dont tell me the answer just show me how to do it
1. C
2. D
3. B
4. A
5. C
D = √a^2 + b^2 + c^2
D = √(10^2 + 4^2 + 10^2)
http://www.ditutor.com/solid_gometry/rectangular_prism.html
thank you
You're welcome.
bruh, really? wtaf is the answer?
To calculate the length of the diagonal of a rectangular prism, also known as the space diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) 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. The length and width are perpendicular to each other, and the height acts as the hypotenuse.
To find the space diagonal, follow these steps:
1. Square the length, width, and height:
- Length^2 = 10^2 = 100
- Width^2 = 4^2 = 16
- Height^2 = 10^2 = 100
2. Add the squared values together:
- 100 + 16 + 100 = 216
3. Take the square root of the sum to find the length of the diagonal:
- √216 ≈ 14.7
Therefore, the length of the diagonal of the given rectangular prism, rounded to the nearest tenth, is approximately 14.7 cm.