Mathematics: (pythagorean theorem) a diagonal of a cube goes from one of the cube s top corners to the opposite corner of the base of the cube. find the length to a diagonal d in a cube that has an edge of length 10 meters.

(pythagorean theorem) a diagonal of a cube goes

Ответ:

bcampos

07.01.2022

First draw a picture (see attached).

You want to find the diagonal of the cube, length AB.
The right triangle formed is trianagle ABD.
AD = 10m

DB will be the hypotenuse of triangle BCD.
$(BC)^2 + (CD)^2 = (DB)^2 \\ 
(10)^2 + (10)^2 = (DB)^2 \\
DB = \sqrt{200}= 10 \sqrt{2}$ .

If we know the length of AD and DB, we can find AB.
$(AD)^2+(BC)^2 = (AB)^2 \\
(10)^2 + (10 \sqrt{2})^2 = (AB)^2 \\
AB = \sqrt{300} = 10 \sqrt{3}$

In fact, the diagonal of any cube is √3 times the side length of the cube.
Let s be the side length (as in AD or CD in the attached) and
h be the hypotenuse of the base, (DB in the attached) and
d be the diagonal of the cube (AB in the attached).

The hypotenuse of the base will be: $s^2+s^2 = h^2 \\
$ .

The cube's diagonal will be:
h^2+s^2 = d^2

.

Substituting s^2+s^2

, you have
$s^2+s^2+s^2 = d^2 \\
3s^2 = d^2 \\
d = \sqrt{3s^2} = s\sqrt{3}$

(pythagorean theorem) a diagonal of a cube goes from one of the cube's top corners to the opposite

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Ответ:

bnnn

08.11.2020

Mathematics

4/9

Step-by-step explanation:

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(pythagorean theorem)
a diagonal of a cube goes from one of the cube's top corners to the opposite corner of the base of the cube. find the length to a diagonal d in a cube that has an edge of length 10 meters.

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(pythagorean theorem) a diagonal of a cube goes from one of the cube's top corners to the opposite corner of the base of the cube. find the length to a diagonal d in a cube that has an edge of length 10 meters.

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(pythagorean theorem)
a diagonal of a cube goes from one of the cube's top corners to the opposite corner of the base of the cube. find the length to a diagonal d in a cube that has an edge of length 10 meters.