# Cuboid face diagonals

The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio?

The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.

Result

y =  0

#### Solution:

$a=5 \ \\ b=10 \ \\ c=15 \ \\ \ \\ a:b:c=1:2:3 \ \\ \ \\ u_{1}=\sqrt{ a^2+b^2 }=\sqrt{ 5^2+10^2 } \doteq 5 \ \sqrt{ 5 } \doteq 11.1803 \ \\ u_{2}=\sqrt{ a^2+c^2 }=\sqrt{ 5^2+15^2 } \doteq 5 \ \sqrt{ 10 } \doteq 15.8114 \ \\ u_{3}=\sqrt{ b^2+c^2 }=\sqrt{ 10^2+15^2 } \doteq 5 \ \sqrt{ 13 } \doteq 18.0278 \ \\ \ \\ k_{1}=u_{1}:u_{2}=11.1803:15.8114 \doteq 0.7071 \ \\ k_{2}=u_{3}:u_{2}=18.0278:15.8114 \doteq 1.1402 \ \\ k_{3}=u_{3}:u_{1}=18.0278:11.1803 \doteq 1.6125 \ \\ \ \\ k_{1},k_{2},k_{3} \ne 1,2,3 \ \\ \ \\ y=0$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Check out our ratio calculator.
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. Wall and body diagonals
The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
2. Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
3. A box
A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R?
4. Find diagonal
Find diagonal of cuboid with length=20m width=25m height=150m
5. Height of the cuboid
Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?
6. Height of the room
Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
7. Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
8. Diagonals in diamons/rhombus
Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
9. Square diagonal
Calculate the length of diagonal of the square with side a = 23 cm.
10. Park
In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m.
11. Median
The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N.
12. Median in right triangle
In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).