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Gwar [14]
3 years ago
15

(PYTHAGOREAN THEOREM)

Mathematics
1 answer:
tiny-mole [99]3 years ago
5 0
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 <em>s</em> 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
<em>d</em> be the diagonal of the cube (AB in the attached).

The hypotenuse of the base will be:s^2+s^2 = h^2 \\&#10;.

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

Substituting s^2+s^2 as h^2, you have
s^2+s^2+s^2 = d^2 \\&#10;3s^2 = d^2 \\&#10;d =  \sqrt{3s^2} =  s\sqrt{3}

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