Question

Help Please! a cube is made up of six congruent square faces . find the length of the inner diagonal (line AH) of the cube. note that AH is the hypotenuse of right triangle ADH

Answer 1

Do you mean, a cube with side length x and you want the length of the diagonal through the center of the cube?

Answer 2

yes please

Answer 3

ok so first you need to find a diagonal across one of the faces of the cube.

Answer 4

its 7cm

Answer 5

where did you get a 7 from?

Answer 6

so using that diagonal as the base of a triangle, the side is length x, you need to find the hypotenuse.

Answer 7

The hypotenuse is the diagonal through the center of the cube.

Answer 8

dose that help?

Answer 9

Ok.. so DH is
\[DH = \sqrt{7^2 + 7^2}\]

Answer 10

DH^2 + AD^2 = AH^2

Answer 11

2?

Answer 12

A side length is 7, the diagonal will be longer than a side length, so 2 is not correct.

Answer 13

oh okay!

Answer 14

so if i round your answer to the nearest hundredth. it would be 8?

Answer 15

the hundredth is the second decimal place

Answer 16

so 8.7? or 8.77?

Answer 17

Okay that makes sense

Answer 18

wait, i misscalculated

Answer 19

so the diagonal line is 8.77cm

Answer 20

no, here.. i misstyped here is the new answer

Answer 21

oh okay..

Answer 22

DH = \[\sqrt{7^2 + 7^2} = 7\sqrt{2}\]
AD = 7
so

\[AH = \sqrt{7^2 + (7\sqrt{2})^2}\]

Answer 23

\[AH = 7\sqrt{3} \approx 12.12\]

Answer 24

mmkay