The edge length of a cube with diagnal of 9 ft. What is the edge length?

liveevillevi
Apr 19, 2017

#1**+2 **

Let's just look at one face of this cube.

(Since it is a cube, all the faces are the exact same.)

The edge length is labeled "s".

Since the diagonal forms the hypotenuse of a right triangle,

and both legs are "s",

we can use the Pythagorean theorem to find s.

s^{2} + s^{2} = 9^{2}

2s^{2} = 81

s^{2} = 40.5

s = \(+\sqrt{40.5} \approx 6.364 \text{ feet}\)

hectictar
Apr 19, 2017

#6**+3 **

Hectictar has given the edge length if the diagonal is across one face of the cube ...DB as shown below.......however.......if the diagonal is considered to be AB....we have...

AB = √[3s^2]

9 = √[3s^2] square both sides

81 = 3 s^2 divide both sides by 3

27 = s^2 take the square root of both sides

3√3 ft = s ≈ 5.19 ft.

CPhill
Apr 19, 2017

#7